크게 3개의 내용으로 구성되어 있음: 1. 논문의 <표 1>의 확장 2. 논문의 <표 2>의 확장 3. 논문의 <표 3>의 확장 =========================================== 1. <표 1>의 확장 =========================================== 약어 설명: n.survey = 각 지역구의 출구조사 표본크기 conf.level = 신뢰수준 n.iter = 신뢰구간의 성능을 알아보기 위한 반복실험횟수 n.sim = 몬테칼로 방법으로 P_i 를 추정할 때 필요한 반복횟수. 100 이상이기만 하면 실험 결과에 별 차이가 없음. K = 각 지역구의 출마자 수 alpdiri = 대칭형 디리클레 분포의 모수 알파의 값 truest = 평균참의석수 (반복실험횟수 n.iter번에 걸쳐 얻어진 참의석수의 평균) predY = 추정량 S의 평균 (반복실험횟수 n.iter번에 걸쳐 얻어진 예상의석수 S의 평균) predPi = 추정량 Sum of Phat_i의 평균 RMSE.Y = 추정량 S의 RMSE (Root Meas Square Error) RMSE.Pi = 추정량 Sum of Phat_i의 RMSE cpsim = 신뢰구간1의 실제신뢰수준 (신뢰구간1은 S의 분산을 추정하기 위해 필요한 P_i의 추정을 몬테칼로 방법으로 함) lensim = 신뢰구간1의 길이 (반복실험횟수 n.iter번에 걸쳐 얻어진 신뢰구간1의 길이의 평균) cpnor1 = 신뢰구간2의 실제신뢰수준 (신뢰구간2는 S의 분산을 추정하기 위해 필요한 P_i의 추정을 정규분포 가정과 함께 귀무가설의 참 가정 하에서 함) lennor1 = 신뢰구간2의 길이 cpnor2 = 신뢰구간3의 실제신뢰수준 (신뢰구간3은 S의 분산을 추정하기 위해 필요한 P_i의 추정을 정규분포 가정과 함께 다항분포의 분산 식 이용) lennor2 = 신뢰구간3의 길이 cpPi = 신뢰구간4의 실제신뢰수준 (신뢰구간4는 점추정량을 Sum of Phat_i 로 하고 분산은 추정량 S의 분산을 그대로 쓴 신뢰구간. 이론적 근거 없음) lenPi = 신뢰구간4의 길이 ------------------------------------------------------------------------------------------------------------------------------ n.survey=2800 conf.level=0.95 ------------------------------------------------------------------------------------------------------------------------------ K= 3, n.iter= 1000, n.sim= 400, n.survey= 2800, conf.level= 0.95 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.33 82.1 82.1 82.2 1.01 0.87 0.901 3.34 0.9 3.34 0.9 3.34 0.947 3.34 (0.2) (0.2) (0.2) (0.04) (0.03) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.007) (0.03) 1 82.1 82.1 82.1 1.51 1.26 0.901 4.85 0.899 4.84 0.899 4.84 0.954 4.85 (0.2) (0.2) (0.2) (0.07) (0.05) (0.009) (0.03) (0.01) (0.03) (0.01) (0.03) (0.007) (0.03) 3 82 81.9 82.2 2.05 1.77 0.901 6.74 0.897 6.7 0.897 6.7 0.949 6.74 (0.2) (0.2) (0.2) (0.09) (0.07) (0.009) (0.02) (0.01) (0.02) (0.01) (0.02) (0.007) (0.02) 9 82.1 82 82.7 2.72 2.37 0.902 9 0.9 8.93 0.9 8.93 0.947 9 (0.2) (0.2) (0.2) (0.14) (0.11) (0.009) (0.02) (0.009) (0.02) (0.009) (0.02) (0.007) (0.02) K= 4, n.iter= 1000, n.sim= 400, n.survey= 2800, conf.level= 0.95 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.25 61.3 61.3 61.3 1.02 0.86 0.896 3.13 0.896 3.13 0.896 3.13 0.935 3.13 (0.2) (0.2) (0.2) (0.04) (0.03) (0.01) (0.03) (0.01) (0.03) (0.01) (0.03) (0.008) (0.03) 1 61.7 61.7 61.8 1.5 1.28 0.903 5.06 0.905 5.03 0.905 5.03 0.953 5.06 (0.2) (0.2) (0.2) (0.06) (0.05) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.007) (0.03) 4 61.4 61.4 61.9 2.33 2.04 0.899 7.52 0.893 7.43 0.893 7.42 0.949 7.52 (0.2) (0.2) (0.2) (0.11) (0.09) (0.01) (0.02) (0.01) (0.02) (0.01) (0.02) (0.007) (0.02) 16 61.6 61.5 63.6 3.19 3.36 0.908 10.82 0.897 10.55 0.897 10.55 0.894 10.82 (0.2) (0.2) (0.2) (0.19) (0.18) (0.009) (0.02) (0.01) (0.02) (0.01) (0.02) (0.01) (0.02) K= 5, n.iter= 1000, n.sim= 400, n.survey= 2800, conf.level= 0.95 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.2 49.1 49.1 49.1 0.89 0.77 0.898 2.84 0.899 2.83 0.899 2.83 0.94 2.84 (0.2) (0.2) (0.2) (0.03) (0.02) (0.01) (0.03) (0.01) (0.03) (0.01) (0.03) (0.008) (0.03) 1 49.1 49 49.2 1.51 1.29 0.916 5.04 0.913 5 0.913 5 0.939 5.04 (0.2) (0.2) (0.2) (0.06) (0.05) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.008) (0.03) 5 49.2 49.1 50.1 2.32 2.22 0.917 8.05 0.91 7.88 0.91 7.88 0.933 8.05 (0.2) (0.2) (0.2) (0.11) (0.11) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.008) (0.03) 25 49 48.8 53.2 3.58 5.23 0.918 12.41 0.909 11.81 0.909 11.81 0.749 12.41 (0.2) (0.2) (0.2) (0.23) (0.29) (0.009) (0.02) (0.009) (0.02) (0.009) (0.02) (0.014) (0.02) K= 6, n.iter= 1000, n.sim= 400, n.survey= 2800, conf.level= 0.95 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.17 41.3 41.3 41.3 0.88 0.74 0.895 2.68 0.894 2.67 0.893 2.67 0.937 2.68 (0.2) (0.2) (0.2) (0.03) (0.02) (0.01) (0.03) (0.01) (0.03) (0.01) (0.03) (0.008) (0.03) 1 41.2 41.1 41.4 1.55 1.27 0.901 5.01 0.9 4.97 0.9 4.97 0.953 5.01 (0.2) (0.2) (0.2) (0.06) (0.05) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.007) (0.03) 6 41 40.9 42.3 2.58 2.59 0.908 8.49 0.891 8.23 0.891 8.23 0.908 8.49 (0.2) (0.2) (0.2) (0.13) (0.13) (0.009) (0.03) (0.01) (0.03) (0.01) (0.03) (0.009) (0.03) 36 41.1 41 48.9 3.87 8.46 0.931 13.97 0.909 12.93 0.909 12.93 0.406 13.97 (0.2) (0.2) (0.2) (0.24) (0.43) (0.008) (0.02) (0.009) (0.02) (0.009) (0.02) (0.016) (0.02) ------------------------------------------------------------------------------------------------------------------------------ conf.level=0.99 ------------------------------------------------------------------------------------------------------------------------------ K= 3, n.iter= 1000, n.sim= 400, n.survey= 2800, conf.level= 0.99 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.33 81.8 81.8 81.8 1.08 0.9 0.967 4.43 0.967 4.43 0.967 4.43 0.992 4.43 (0.2) (0.2) (0.2) (0.04) (0.03) (0.006) (0.04) (0.006) (0.04) (0.006) (0.04) (0.003) (0.04) 1 82 82.1 82.1 1.52 1.28 0.968 6.39 0.967 6.38 0.967 6.38 0.992 6.39 (0.2) (0.2) (0.2) (0.07) (0.05) (0.006) (0.03) (0.006) (0.04) (0.006) (0.04) (0.003) (0.03) 3 82.3 82.2 82.5 2.05 1.7 0.967 8.9 0.965 8.85 0.965 8.85 0.993 8.9 (0.2) (0.2) (0.2) (0.1) (0.07) (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) (0.003) (0.03) 9 82 82 82.6 2.74 2.38 0.973 11.86 0.97 11.76 0.97 11.76 0.99 11.86 (0.2) (0.2) (0.2) (0.14) (0.12) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) K= 4, n.iter= 1000, n.sim= 400, n.survey= 2800, conf.level= 0.99 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.25 61.6 61.6 61.6 0.97 0.81 0.965 4.03 0.967 4.03 0.967 4.02 0.984 4.03 (0.2) (0.2) (0.2) (0.04) (0.03) (0.006) (0.04) (0.006) (0.04) (0.006) (0.04) (0.004) (0.04) 1 61.5 61.5 61.6 1.49 1.25 0.976 6.55 0.972 6.52 0.972 6.52 0.994 6.55 (0.2) (0.2) (0.2) (0.07) (0.05) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.002) (0.03) 4 61.4 61.4 61.9 2.33 2 0.963 9.83 0.962 9.71 0.962 9.7 0.987 9.83 (0.2) (0.2) (0.2) (0.12) (0.09) (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) (0.004) (0.03) 16 61.7 61.5 63.6 3.29 3.38 0.962 14.24 0.957 13.88 0.957 13.88 0.967 14.24 (0.2) (0.2) (0.2) (0.19) (0.2) (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) K= 5, n.iter= 1000, n.sim= 400, n.survey= 2800, conf.level= 0.99 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.2 49.2 49.3 49.3 0.88 0.73 0.97 3.78 0.972 3.78 0.972 3.78 0.987 3.78 (0.2) (0.2) (0.2) (0.03) (0.02) (0.005) (0.04) (0.005) (0.04) (0.005) (0.04) (0.004) (0.04) 1 49 49 49.2 1.5 1.26 0.969 6.56 0.97 6.5 0.97 6.5 0.989 6.56 (0.2) (0.2) (0.2) (0.06) (0.05) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 5 49 49 49.9 2.32 2.18 0.983 10.55 0.98 10.33 0.98 10.33 0.99 10.55 (0.2) (0.2) (0.2) (0.12) (0.1) (0.004) (0.03) (0.004) (0.03) (0.004) (0.03) (0.003) (0.03) 25 49.4 49.3 53.7 3.6 5.32 0.979 16.37 0.971 15.59 0.971 15.58 0.889 16.37 (0.2) (0.2) (0.2) (0.22) (0.3) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.01) (0.03) K= 6, n.iter= 1000, n.sim= 400, n.survey= 2800, conf.level= 0.99 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.17 40.8 40.8 40.8 0.85 0.74 0.963 3.52 0.966 3.52 0.966 3.52 0.983 3.52 (0.2) (0.2) (0.2) (0.03) (0.03) (0.006) (0.04) (0.006) (0.04) (0.006) (0.04) (0.004) (0.04) 1 40.8 40.7 41 1.52 1.27 0.975 6.61 0.973 6.54 0.973 6.53 0.989 6.61 (0.2) (0.2) (0.2) (0.06) (0.05) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 6 40.7 40.5 42 2.45 2.5 0.981 11.1 0.976 10.74 0.976 10.74 0.979 11.1 (0.2) (0.2) (0.2) (0.12) (0.12) (0.004) (0.03) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) 36 40.8 40.6 48.4 3.84 8.34 0.984 18.24 0.972 16.87 0.972 16.86 0.687 18.24 (0.2) (0.2) (0.2) (0.25) (0.41) (0.004) (0.03) (0.005) (0.03) (0.005) (0.03) (0.015) (0.03) -------------------------------------------------------------------------------------------------------------- n.survey=500 conf.level=0.95 -------------------------------------------------------------------------------------------------------------- K= 3, n.iter= 1000, n.sim= 400, n.survey= 500, conf.level= 0.95 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.33 81.3 81.4 81.6 1.68 1.44 0.884 5.27 0.882 5.25 0.882 5.24 0.941 5.27 (0.2) (0.2) (0.2) (0.08) (0.06) (0.01) (0.02) (0.01) (0.02) (0.01) (0.02) (0.007) (0.02) 1 82 81.8 82.4 2.3 2.01 0.906 7.61 0.904 7.56 0.904 7.55 0.948 7.61 (0.2) (0.2) (0.2) (0.11) (0.09) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.007) (0.03) 3 82 81.7 83.2 3.1 2.85 0.922 10.4 0.915 10.27 0.915 10.26 0.927 10.4 (0.2) (0.2) (0.2) (0.18) (0.15) (0.008) (0.02) (0.009) (0.02) (0.009) (0.02) (0.008) (0.02) 9 82.1 81.5 85.2 4.19 4.74 0.907 13.82 0.899 13.54 0.899 13.53 0.856 13.82 (0.2) (0.2) (0.2) (0.3) (0.3) (0.009) (0.02) (0.01) (0.02) (0.01) (0.02) (0.011) (0.02) K= 4, n.iter= 1000, n.sim= 400, n.survey= 500, conf.level= 0.95 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.25 61.6 61.6 61.7 1.57 1.35 0.887 4.89 0.883 4.87 0.882 4.86 0.925 4.89 (0.2) (0.2) (0.2) (0.07) (0.06) (0.01) (0.03) (0.01) (0.03) (0.01) (0.03) (0.008) (0.03) 1 61.4 61.3 62.1 2.36 2.08 0.901 7.82 0.899 7.71 0.899 7.7 0.949 7.82 (0.2) (0.2) (0.2) (0.12) (0.1) (0.009) (0.03) (0.01) (0.03) (0.01) (0.03) (0.007) (0.03) 4 61.4 61 64.1 3.37 3.94 0.921 11.64 0.914 11.3 0.913 11.28 0.858 11.64 (0.2) (0.2) (0.2) (0.21) (0.22) (0.009) (0.02) (0.009) (0.02) (0.009) (0.02) (0.011) (0.02) 16 61.6 60.6 70.7 5.03 9.93 0.905 16.57 0.88 15.73 0.88 15.72 0.396 16.57 (0.2) (0.2) (0.2) (0.34) (0.54) (0.009) (0.02) (0.01) (0.02) (0.01) (0.02) (0.015) (0.02) K= 5, n.iter= 1000, n.sim= 400, n.survey= 500, conf.level= 0.95 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.2 49.4 49.4 49.6 1.32 1.16 0.919 4.57 0.917 4.54 0.916 4.54 0.954 4.57 (0.2) (0.2) (0.2) (0.05) (0.04) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.007) (0.03) 1 49.2 49 50.2 2.39 2.22 0.904 7.88 0.897 7.71 0.896 7.7 0.929 7.88 (0.2) (0.2) (0.2) (0.12) (0.11) (0.009) (0.02) (0.01) (0.02) (0.01) (0.02) (0.008) (0.02) 5 49.2 48.5 53.8 3.71 5.62 0.913 12.62 0.895 11.97 0.893 11.96 0.688 12.62 (0.2) (0.2) (0.2) (0.23) (0.3) (0.009) (0.02) (0.01) (0.02) (0.01) (0.02) (0.015) (0.02) 25 49.4 48.1 67.3 5.46 18.54 0.911 18.85 0.878 17.26 0.876 17.24 0.038 18.85 (0.2) (0.2) (0.2) (0.39) (0.89) (0.009) (0.02) (0.01) (0.02) (0.01) (0.02) (0.006) (0.02) K= 6, n.iter= 1000, n.sim= 400, n.survey= 500, conf.level= 0.95 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.17 41.2 41.2 41.4 1.3 1.16 0.907 4.26 0.904 4.23 0.904 4.22 0.943 4.26 (0.2) (0.2) (0.2) (0.05) (0.04) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.007) (0.03) 1 41 40.7 42.1 2.37 2.26 0.912 7.93 0.899 7.7 0.899 7.69 0.917 7.93 (0.2) (0.2) (0.2) (0.12) (0.11) (0.009) (0.03) (0.01) (0.03) (0.01) (0.03) (0.009) (0.03) 6 41.4 40.7 48.4 3.8 7.69 0.927 13.51 0.905 12.5 0.904 12.48 0.48 13.51 (0.2) (0.2) (0.2) (0.22) (0.4) (0.008) (0.02) (0.009) (0.02) (0.009) (0.02) (0.016) (0.02) 36 40.9 39.4 68.6 5.58 28.13 0.94 20.67 0.907 18.27 0.906 18.25 0.001 20.67 (0.2) (0.2) (0.2) (0.44) (1.17) (0.008) (0.02) (0.009) (0.02) (0.009) (0.02) (0.001) (0.02) -------------------------------------------------------------------------------------------------------------- conf.level=0.99 -------------------------------------------------------------------------------------------------------------- K= 3, n.iter= 1000, n.sim= 400, n.survey= 500, conf.level= 0.99 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.33 81.9 81.8 82 1.6 1.34 0.966 6.82 0.966 6.81 0.966 6.8 0.983 6.82 (0.2) (0.2) (0.2) (0.07) (0.05) (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) (0.004) (0.03) 1 81.8 81.6 82.2 2.31 1.98 0.973 9.96 0.973 9.9 0.972 9.89 0.99 9.96 (0.2) (0.2) (0.2) (0.12) (0.09) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 3 81.7 81.4 82.9 3.09 2.89 0.972 13.65 0.969 13.48 0.969 13.46 0.984 13.65 (0.2) (0.2) (0.2) (0.19) (0.15) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.004) (0.03) 9 82.1 81.5 85.1 4.23 4.6 0.97 18.15 0.963 17.78 0.963 17.76 0.958 18.15 (0.2) (0.2) (0.2) (0.27) (0.28) (0.005) (0.03) (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) K= 4, n.iter= 1000, n.sim= 400, n.survey= 500, conf.level= 0.99 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.25 61.4 61.4 61.6 1.52 1.28 0.962 6.42 0.962 6.39 0.962 6.38 0.992 6.42 (0.2) (0.2) (0.2) (0.07) (0.05) (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) (0.003) (0.03) 1 61.6 61.4 62.2 2.39 2.09 0.97 10.27 0.966 10.13 0.966 10.12 0.993 10.27 (0.2) (0.2) (0.2) (0.12) (0.09) (0.005) (0.03) (0.006) (0.03) (0.006) (0.03) (0.003) (0.03) 4 61.9 61.2 64.4 3.55 3.88 0.969 15.32 0.966 14.87 0.966 14.86 0.963 15.32 (0.2) (0.2) (0.2) (0.21) (0.23) (0.005) (0.03) (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) 16 61.6 60.8 70.8 4.86 10.03 0.98 21.76 0.971 20.66 0.971 20.64 0.644 21.76 (0.2) (0.2) (0.2) (0.32) (0.54) (0.004) (0.03) (0.005) (0.03) (0.005) (0.03) (0.015) (0.03) K= 5, n.iter= 1000, n.sim= 400, n.survey= 500, conf.level= 0.99 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.2 49.4 49.3 49.5 1.4 1.2 0.969 5.98 0.969 5.93 0.969 5.93 0.987 5.98 (0.2) (0.2) (0.2) (0.06) (0.05) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.004) (0.03) 1 49.1 48.9 50 2.33 2.23 0.974 10.44 0.971 10.21 0.971 10.2 0.991 10.44 (0.2) (0.2) (0.2) (0.11) (0.1) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 5 49.4 48.7 54.1 3.67 5.6 0.979 16.62 0.972 15.76 0.972 15.74 0.883 16.62 (0.2) (0.2) (0.2) (0.22) (0.29) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.01) (0.03) 25 49.1 47.9 67 5.41 18.45 0.979 24.75 0.965 22.64 0.965 22.62 0.12 24.75 (0.2) (0.2) (0.2) (0.4) (0.87) (0.005) (0.02) (0.006) (0.03) (0.006) (0.03) (0.01) (0.02) K= 6, n.iter= 1000, n.sim= 400, n.survey= 500, conf.level= 0.99 alpdiri truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.17 41 41 41.1 1.29 1.09 0.969 5.61 0.966 5.57 0.966 5.56 0.99 5.61 (0.2) (0.2) (0.2) (0.05) (0.04) (0.005) (0.03) (0.006) (0.03) (0.006) (0.03) (0.003) (0.03) 1 40.7 40.5 41.9 2.33 2.29 0.976 10.42 0.973 10.12 0.973 10.11 0.985 10.42 (0.2) (0.2) (0.2) (0.12) (0.1) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.004) (0.03) 6 40.9 40.4 48.1 3.55 7.85 0.991 17.73 0.986 16.4 0.986 16.38 0.718 17.73 (0.2) (0.2) (0.2) (0.2) (0.39) (0.003) (0.03) (0.004) (0.03) (0.004) (0.03) (0.014) (0.03) 36 41.1 39.4 68.8 5.67 28.08 0.98 27.2 0.963 24.04 0.963 24.02 0.003 27.2 (0.2) (0.2) (0.2) (0.44) (1.13) (0.004) (0.02) (0.006) (0.02) (0.006) (0.02) (0.002) (0.02) ======================================== 2. <표 2>의 확장 ======================================== -------------------------------------------------------------------------------------------------------------- 실제자료.R의 실행 결과 약어 설명: n.survey = 각 지역구의 출구조사 표본크기 3개의 신뢰구간은 P_i를 구하는 방법에 따라 달라지는 신뢰구간임. 별 차이가 없음을 알 수 있음. -------------------------------------------------------------------------------------------------------------- 실제의석수 무소속 민주통합당 새누리당 자유선진당 통합진보당 3 106 127 3 7 n.survey= 2800 새누리당 예상의석수 = 114 114.9; 95% 신뢰구간 = (109.25,118.75) (109.25,118.75) (109.25,118.75) 민주통합당 예상의석수 = 119 118.1; 95% 신뢰구간 = (114.6,123.4) (114.59,123.41) (114.59,123.41) 통합진보당 예상의석수 = 9 8.7; 95% 신뢰구간 = (7.09,10.91) (7.08,10.92) (7.08,10.92) n.survey= 500 새누리당 예상의석수 = 114 115; 95% 신뢰구간 = (107.14,120.86) (107.13,120.87) (107.13,120.87) 민주통합당 예상의석수 = 119 117.5; 95% 신뢰구간 = (112.54,125.46) (112.55,125.45) (112.55,125.45) 통합진보당 예상의석수 = 9 8.9; 95% 신뢰구간 = (6.26,11.74) (6.22,11.78) (6.22,11.78) n.survey= 2800 새누리당 예상의석수 = 114 114.8; 99% 신뢰구간 = (107.75,120.25) (107.76,120.24) (107.76,120.24) 민주통합당 예상의석수 = 119 118.1; 99% 신뢰구간 = (113.22,124.78) (113.2,124.8) (113.2,124.8) 통합진보당 예상의석수 = 9 8.7; 99% 신뢰구간 = (6.45,11.55) (6.48,11.52) (6.48,11.52) n.survey= 500 새누리당 예상의석수 = 114 115.2; 99% 신뢰구간 = (104.98,123.02) (104.97,123.03) (104.98,123.02) 민주통합당 예상의석수 = 119 117.5; 99% 신뢰구간 = (110.55,127.45) (110.52,127.48) (110.53,127.47) 통합진보당 예상의석수 = 9 8.8; 99% 신뢰구간 = (5.35,12.65) (5.35,12.65) (5.35,12.65) ======================================== 2. <표 3>의 확장 ======================================== -------------------------------------------------------------------------------------------------------------------------------------------------- 실제자료에 가까운 모의실험 결과 약어 설명: n.iter = 신뢰구간의 성능을 알아보기 위한 반복실험횟수 n.survey = 각 지역구의 출구조사 표본크기 n.sim = 몬테칼로 방법으로 P_i 를 추정할 때 필요한 반복횟수. 100 이상이기만 하면 실험 결과에 별 차이가 없음. variation = 모의실험에서 생성되는 실제득표율의 변동 정도. variation이 작아질수록 관측된 예상득표율에 밀집 분포하게 됨 conflev = 신뢰수준 truest = 평균참의석수 (반복실험횟수 n.iter번에 걸쳐 얻어진 참의석수의 평균) predY = 추정량 S의 평균 (반복실험횟수 n.iter번에 걸쳐 얻어진 예상의석수 S의 평균) predPi = 추정량 Sum of Phat_i의 평균 RMSE.Y = 추정량 S의 RMSE (Root Meas Square Error) RMSE.Pi = 추정량 Sum of Phat_i의 RMSE cpsim = 신뢰구간1의 실제신뢰수준 (신뢰구간1은 S의 분산을 추정하기 위해 필요한 P_i의 추정을 몬테칼로 방법으로 함) lensim = 신뢰구간1의 길이 (반복실험횟수 n.iter번에 걸쳐 얻어진 신뢰구간1의 길이의 평균) cpnor1 = 신뢰구간2의 실제신뢰수준 (신뢰구간2는 S의 분산을 추정하기 위해 필요한 P_i의 추정을 정규분포 가정과 함께 귀무가설의 참 가정 하에서 함) lennor1 = 신뢰구간2의 길이 cpnor2 = 신뢰구간3의 실제신뢰수준 (신뢰구간3은 S의 분산을 추정하기 위해 필요한 P_i의 추정을 정규분포 가정과 함께 다항분포의 분산 식 이용) lennor2 = 신뢰구간3의 길이 cpPi = 신뢰구간4의 실제신뢰수준 (신뢰구간4는 점추정량을 Sum of Phat_i 로 하고 분산은 추정량 S의 분산을 그대로 쓴 신뢰구간. 이론적 근거 없음) lenPi = 신뢰구간4의 길이 -------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------- 95% 신뢰구간 ------------------------------------------------------------------------------------------------------------- 새누리당 variation= high (n.survey= 2800 n.iter= 1000, n.sim= 400) conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 104.9 104.9 104.9 0.98 0.82 0.904 3.26 0.904 3.26 0.904 3.26 0.957 3.26 (0.2) (0.2) (0.2) (0.03) (0.03) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.006) (0.03) 새누리당 variation= medium conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 110.1 110.1 110.2 1.41 1.18 0.915 4.71 0.916 4.72 0.916 4.71 0.95 4.71 (0.2) (0.2) (0.2) (0.06) (0.04) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.007) (0.03) 새누리당 variation= low conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 115.8 115.8 115.9 1.84 1.51 0.906 6.1 0.906 6.11 0.906 6.1 0.961 6.1 (0.2) (0.2) (0.2) (0.08) (0.06) (0.009) (0.02) (0.009) (0.02) (0.009) (0.02) (0.006) (0.02) 새누리당 variation= verylow conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 117.9 117.7 117.9 2.17 1.78 0.896 7.14 0.899 7.14 0.898 7.14 0.949 7.14 (0.2) (0.2) (0.2) (0.1) (0.07) (0.01) (0.02) (0.01) (0.02) (0.01) (0.02) (0.007) (0.02) 새누리당 variation= extremelylow conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 116.2 116.2 116.5 2.59 2.23 0.89 8.4 0.891 8.41 0.891 8.4 0.937 8.4 (0.1) (0.1) (0.1) (0.13) (0.1) (0.01) (0.02) (0.01) (0.02) (0.01) (0.02) (0.008) (0.02) ------------------------------------------------------------------------------------------------------------- 99% 신뢰구간 ------------------------------------------------------------------------------------------------------------- 새누리당 variation= high (n.survey= 2800, n.iter= 1000, n.sim= 400) conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.99 104.5 104.4 104.5 1.02 0.86 0.959 4.24 0.96 4.24 0.96 4.24 0.981 4.24 (0.2) (0.2) (0.2) (0.04) (0.03) (0.006) (0.04) (0.006) (0.04) (0.006) (0.04) (0.004) (0.04) 새누리당 variation= medium conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.99 110.2 110.2 110.3 1.46 1.24 0.966 6.27 0.967 6.27 0.967 6.27 0.989 6.27 (0.2) (0.2) (0.2) (0.06) (0.05) (0.006) (0.04) (0.006) (0.04) (0.006) (0.04) (0.003) (0.04) 새누리당 variation= low conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.99 116 116 116.1 1.89 1.59 0.97 7.99 0.97 7.99 0.97 7.99 0.988 7.99 (0.2) (0.2) (0.2) (0.08) (0.06) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 새누리당 variation= verylow conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.99 117.9 117.9 118 2.24 1.89 0.973 9.38 0.974 9.39 0.974 9.39 0.99 9.38 (0.2) (0.2) (0.2) (0.12) (0.09) (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 새누리당 variation= extremelylow conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.99 116.1 116.3 116.5 2.6 2.2 0.968 11.04 0.969 11.05 0.969 11.05 0.987 11.04 (0.1) (0.1) (0.1) (0.14) (0.1) (0.006) (0.03) (0.005) (0.03) (0.005) (0.03) (0.004) (0.03) --------------------------------------------------------------------------------------------------------------------- 같은 실험에서 95%와 99% 두 신뢰구간을 동시에 구해 출력. 따라서 두 신뢰구간의 truest, pred, RMSE는 같다; n.survey=2800 --------------------------------------------------------------------------------------------------------------------- 새누리당 variation= high (n.survey= 2800 n.iter= 1000, n.sim= 400) conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 104.9 104.9 104.9 0.98 0.82 0.904 3.26 0.904 3.26 0.904 3.26 0.957 3.26 (0.2) (0.2) (0.2) (0.03) (0.03) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.006) (0.03) 0.99 0.978 4.28 0.978 4.28 0.978 4.28 0.993 4.28 (0.005) (0.04) (0.005) (0.03) (0.005) (0.03) (0.003) (0.04) 새누리당 variation= medium conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 110.1 110.1 110.2 1.41 1.18 0.915 4.71 0.916 4.72 0.916 4.71 0.95 4.71 (0.2) (0.2) (0.2) (0.06) (0.04) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.007) (0.03) 0.99 0.972 6.2 0.973 6.2 0.973 6.2 0.992 6.2 (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 새누리당 variation= low conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 115.8 115.8 115.9 1.84 1.51 0.906 6.1 0.906 6.11 0.906 6.1 0.961 6.1 (0.2) (0.2) (0.2) (0.08) (0.06) (0.009) (0.02) (0.009) (0.02) (0.009) (0.02) (0.006) (0.02) 0.99 0.967 8.02 0.969 8.02 0.969 8.02 0.994 8.02 (0.006) (0.03) (0.005) (0.03) (0.005) (0.03) (0.002) (0.03) 새누리당 variation= verylow conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 117.9 117.7 117.9 2.17 1.78 0.896 7.14 0.899 7.14 0.898 7.14 0.949 7.14 (0.2) (0.2) (0.2) (0.1) (0.07) (0.01) (0.02) (0.01) (0.02) (0.01) (0.02) (0.007) (0.02) 0.99 0.969 9.38 0.969 9.39 0.969 9.38 0.991 9.38 (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 새누리당 variation= extremelylow conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 116.2 116.2 116.5 2.59 2.23 0.89 8.4 0.891 8.41 0.891 8.4 0.937 8.4 (0.1) (0.1) (0.1) (0.13) (0.1) (0.01) (0.02) (0.01) (0.02) (0.01) (0.02) (0.008) (0.02) 0.99 0.972 11.04 0.973 11.05 0.973 11.04 0.992 11.04 (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 민주통합당 variation= high (n.survey= 2800 n.iter= 1000, n.sim= 400) conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 96.9 96.9 96.9 0.96 0.8 0.917 3.05 0.913 3.05 0.913 3.05 0.952 3.05 (0.2) (0.2) (0.2) (0.04) (0.03) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.007) (0.03) 0.99 0.962 4 0.961 4 0.961 4 0.985 4 (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) (0.004) (0.03) 민주통합당 variation= medium conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 100.4 100.4 100.5 1.41 1.17 0.895 4.51 0.892 4.51 0.892 4.51 0.956 4.51 (0.2) (0.2) (0.2) (0.06) (0.04) (0.01) (0.03) (0.01) (0.03) (0.01) (0.03) (0.006) (0.03) 0.99 0.965 5.92 0.964 5.92 0.964 5.92 0.993 5.92 (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) (0.003) (0.03) 민주통합당 variation= low conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 106 106 106 1.78 1.51 0.904 5.87 0.905 5.87 0.905 5.87 0.95 5.87 (0.2) (0.2) (0.2) (0.07) (0.06) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.007) (0.03) 0.99 0.969 7.71 0.969 7.71 0.969 7.71 0.99 7.71 (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 민주통합당 variation= verylow conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 109.7 109.4 109.6 2.1 1.73 0.907 6.86 0.908 6.86 0.908 6.86 0.952 6.86 (0.2) (0.2) (0.2) (0.1) (0.08) (0.009) (0.02) (0.009) (0.02) (0.009) (0.02) (0.007) (0.02) 0.99 0.975 9.01 0.976 9.02 0.976 9.02 0.988 9.01 (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 민주통합당 variation= extremelylow conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 115.1 114.8 114.7 2.42 2.06 0.898 8.01 0.898 8.02 0.898 8.02 0.951 8.01 (0.1) (0.1) (0.1) (0.12) (0.09) (0.01) (0.02) (0.01) (0.02) (0.01) (0.02) (0.007) (0.02) 0.99 0.971 10.53 0.971 10.54 0.971 10.54 0.989 10.53 (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) -------------------------------------------------------------------------------------------------------------------- n.survey=500 -------------------------------------------------------------------------------------------------------------------- 새누리당 variation= high (n.survey= 500, n.iter= 1000, n.sim= 400) conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 104.6 104.5 104.7 1.54 1.3 0.901 5.04 0.904 5.04 0.903 5.03 0.948 5.04 (0.2) (0.2) (0.2) (0.06) (0.05) (0.009) (0.03) (0.009) (0.03) (0.009) (0.03) (0.007) (0.03) 0.99 0.967 6.62 0.967 6.62 0.967 6.61 0.989 6.62 (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) (0.003) (0.03) 새누리당 variation= medium conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 110 109.7 110.2 2.31 1.9 0.896 7.38 0.896 7.37 0.895 7.37 0.95 7.38 (0.2) (0.2) (0.2) (0.12) (0.08) (0.01) (0.02) (0.01) (0.02) (0.01) (0.02) (0.007) (0.02) 0.99 0.965 9.7 0.964 9.69 0.964 9.68 0.992 9.7 (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) (0.003) (0.03) 새누리당 variation= low conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 116.1 115.8 116.4 2.75 2.36 0.909 9.36 0.91 9.35 0.909 9.34 0.959 9.36 (0.2) (0.2) (0.2) (0.14) (0.11) (0.009) (0.02) (0.009) (0.02) (0.009) (0.02) (0.006) (0.02) 0.99 0.977 12.3 0.977 12.29 0.977 12.28 0.989 12.3 (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 새누리당 variation= verylow conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 117.9 117.5 118.3 3.27 2.79 0.912 10.9 0.911 10.9 0.91 10.89 0.943 10.9 (0.2) (0.2) (0.2) (0.19) (0.15) (0.009) (0.02) (0.009) (0.02) (0.009) (0.02) (0.007) (0.02) 0.99 0.97 14.32 0.97 14.33 0.97 14.31 0.988 14.32 (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 새누리당 variation= extremelylow conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 116.1 116 117.3 3.79 3.31 0.907 12.63 0.907 12.64 0.907 12.62 0.952 12.63 (0.1) (0.1) (0.1) (0.23) (0.19) (0.009) (0.02) (0.009) (0.02) (0.009) (0.02) (0.007) (0.02) 0.99 0.98 16.6 0.98 16.61 0.98 16.59 0.988 16.6 (0.004) (0.02) (0.004) (0.02) (0.004) (0.02) (0.003) (0.02) 민주통합당 variation= high (n.survey= 500, n.iter= 1000, n.sim= 400) conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 96.5 96.3 96.6 1.42 1.23 0.921 4.83 0.921 4.82 0.921 4.82 0.956 4.83 (0.2) (0.2) (0.2) (0.06) (0.05) (0.009) (0.02) (0.009) (0.02) (0.009) (0.02) (0.006) (0.02) 0.99 0.975 6.34 0.975 6.34 0.975 6.33 0.991 6.34 (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 민주통합당 variation= medium conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 100.6 100.4 100.8 2.18 1.86 0.896 7 0.893 6.99 0.892 6.98 0.948 7 (0.2) (0.2) (0.2) (0.1) (0.08) (0.01) (0.03) (0.01) (0.03) (0.01) (0.03) (0.007) (0.03) 0.99 0.966 9.19 0.965 9.18 0.965 9.17 0.99 9.19 (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) (0.003) (0.03) 민주통합당 variation= low conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 106.1 105.9 106.4 2.78 2.29 0.891 8.99 0.892 8.98 0.891 8.97 0.957 8.99 (0.2) (0.2) (0.2) (0.14) (0.11) (0.01) (0.02) (0.01) (0.02) (0.01) (0.02) (0.006) (0.02) 0.99 0.977 11.81 0.976 11.8 0.976 11.79 0.992 11.81 (0.005) (0.03) (0.005) (0.03) (0.005) (0.03) (0.003) (0.03) 민주통합당 variation= verylow conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 109.5 109 109.5 3.28 2.72 0.885 10.51 0.884 10.51 0.883 10.5 0.945 10.51 (0.2) (0.2) (0.2) (0.19) (0.14) (0.01) (0.02) (0.01) (0.02) (0.01) (0.02) (0.007) (0.02) 0.99 0.967 13.81 0.967 13.82 0.967 13.8 0.993 13.81 (0.006) (0.03) (0.006) (0.03) (0.006) (0.03) (0.003) (0.03) 민주통합당 variation= extremelylow conflev truest predY predPi RMSE.Y RMSE.Pi cpsim lensim cpnor1 lennor1 cpnor2 lennor2 cpPi lenPi 0.95 114.9 113.7 113.8 3.87 3.21 0.894 12.09 0.895 12.12 0.895 12.1 0.937 12.09 (0.1) (0.1) (0.1) (0.24) (0.18) (0.01) (0.02) (0.01) (0.02) (0.01) (0.02) (0.008) (0.02) 0.99 0.962 15.89 0.962 15.92 0.962 15.9 0.987 15.89 (0.006) (0.02) (0.006) (0.02) (0.006) (0.02) (0.004) (0.02)