9920109 2 15 1 24 80 19203937421 ebaku24@gmail.com 1 1 20
1 2 3 4 5 5 h1,, 5 j1,, J h h j 1 y hj w hj j yˇ hj w hj y hj Jh ˆMh whj j 1 Mˆ hmˆ h' J h j1yˇ hj ˆh h1,, 5 Mˆ h Mean of WeekdayMW 1 MW 5 h1 ˆ+ 1 ˆh 1.1 5 1 2 2 Mean with the Pooled Data MP ˆ+ MP 5 h1 5 h1 J h j1yˇ hj Mˆ h 1.2 MW Mˆ h Mˆ h' MW MP ˆ+ MW ˆ+ MP ˆ+ MW MP ˆ+ 3 MP MW 4 MW 21
9920109 47 2 8 5 80 80 6 MW 2 1 h1,, 7 h1 1 5i1,, m h j1,, n hi hij 0, 1 hij 1 7 B h f re 4/5 w hkgi w hkgi Nˆ h 2.1 1 re w hij hijj w hkgi f B h 2.1 hijj B h Nˆ h kgijjh w hkgi 1 y hij Nˆ h ij w hij hij Ŷ h ij w hijy hij MW Ŷ h h Nˆ h 2.2 MW ~ MW 2 8 i 22
k1k 1995 g1g k G k k f 1 kg GC k C C kg k g C k k k kg i1m kg m kg k g f 2 kg m M M kg kg kg kg q1qq8 g1g qkg hk 8 f 3 q 1/8 f 3 f 2f f 5f f h1 4 3 3 h5 q 3 3 h6,7 q 3 q f re 4/5 h1l i1m h hij {0, 1} j1, n hi hij 1 re whij hij whkgi 1/f B h hij j w ˆN hkgi r 1 2 3 kg h fkgfkgfh B h r kg kg 1 2003pp.911913 m h m kg 8 hij w hkgi Household ClusterHC 2 9 23
9920109 MW HC 1011 Vˆ hvˆˆ 2 h+ +2 q Covˆ hq, ˆ h'q Vˆˆ h+ mh+ 1 m h+ 1 Nˆ 2 h ih ji w hijy hij ˆ h+ 2 Covˆ hq, ˆ h'q mq+ 1 m q+ 1 Nˆ hnˆ ih jiw hijy hij ˆ h jiw hijy hij ˆ h' h' 2.3 2.4 2.5 2.3MW 2.5 12 HC HC 2.3 1 1 2.3 45 2.3 HC 45 13 2.3 HC 100.0 10.0 1.0 0.1 1.0 10.0 100.0 0.1 総数 男 男 (10-14 歳 ) 男 (40-44 歳 ) 男 (80 歳 -) 1 HC 10 5 24
14 MP MW MP HC 15 MP MW v hij w hij Nˆ h 3.1 ijjh v hij1 ijjh w hijnˆ h 1 MW MP ˆ MW v ˆ v hijv hijy hij 1 Ŷ h h 3.2 hij v hij hij Nˆ h MP HC MW HC 2.3 Vˆˆ v v hvˆˆh 2 +2 qcovˆh v Vˆ v Vˆˆh Vˆˆ v Covˆh v q, ˆh h+ v q, ˆh q q Covˆ hq, ˆ hq 3.3 MW 2.3 3.3 HC HC 2 HC 4 16 25
9920109 HPHousehold cluster for the pooled datahp 3.3 Vˆˆ v HC m + 2 m + 1 i hji w hij Nˆ h y hij ˆ v 2 4.1 SHPHousehold cluster stratified by days for the pooled data SHP HC v ˆh Vˆˆ v SHC h 2 ih ji w hij Nˆ h m h m h 1 y hij ˆ v 2 1 v h ˆh ˆ 2 m h 1 v 2 RGRandom groups 17 4.2 2003 4 k4 4 1 2 ˆV ˆ RG k ˆkˆ 4 1 SE V ˆ ˆ RG / 4 4.3 JKThe deleteone jackknife 18 1 2 i m + m + 1 v hij i ˆ i i ˆ i m ˆ i /n Vˆˆ v JK n1 m ˆ i ˆ 2 n 4.4 4 HC 2 2001 19 m h 20 m h 26
(%) 35 30 25 20 15 10 5 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0 0 50 100 150 200 250 300 ( 世帯数 ) HC RG1 HP RG2 SHP ウェイト無 JK1 0.00 0 50 100 150 200 250 300 ( 世帯数 ) Cor1 * Cor2 * Cor1 * +Cor2 * 21 HC 3.3HP 4.1SHP 4.2 4.3 4.4 HCHPSHPRG1RG2 JK1 2 RG1 RG2 2 200 HP 1002001 4020 HC SHP HC 100 50 50 HP SHP HC 200 1 2 22 3 2 Cor1 0.6 Cor2 100 SHP HC HP 27
9920109 HP SHP HP HP 1 2 13 2009 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a 0.09 0.38 0.30 0.29 0.28 1.53 0.53 5.78 2.62 1.31 0.90 0.51 0.49 1.37 1.81 1.36 4.08 2.03 2.16 1.83 0.15 0.60 0.27 0.35 0.36 2.30 1.81 10.20 3.48 3.13 1.06 0.52 0.47 1.09 1.80 0.97 5.86 2.77 1.06 1.79 1014 0.17 0.82 0.89 0.96 46.23 0.95 11.89 146.93 49.03 12.57 6.14 2.93 1.94 1.47 3.04 3.46 17.10 5.76 27.25 4.32 4044 0.36 2.20 1.06 0.97 0.44 72.99 5.02 18.63 9.59 3.65 2.71 1.73 1.71 8.15 5.22 7.27 11.25 3.12 10.56 2.88 80 0.54 2.03 0.75 22.29 11.80 166.55 8.31 26.00 130.96 7.65 8.15 1.53 2.30 26.61 3.27 13.03 10.79 4.80 5.09 11.09 HC b 0.12 0.56 0.28 0.61 0.40 1.59 4.31 14.37 16.04 3.29 1.37 0.56 0.68 2.03 1.19 1.62 4.59 1.78 3.05 2.36 0.16 0.65 0.35 0.96 0.61 2.12 2.42 9.92 5.70 2.35 1.72 0.78 0.91 3.01 1.88 2.44 6.58 2.29 3.96 3.14 1014 0.39 1.80 0.88 2.18 34.07 0.95 16.24 51.43 44.02 11.73 6.60 2.34 2.27 4.71 4.78 4.78 22.72 9.88 24.41 9.89 4044 0.51 2.51 1.21 2.60 1.17 52.35 10.50 46.09 14.75 10.69 6.71 3.07 3.60 16.18 9.84 13.75 20.33 9.58 17.43 11.34 80 1.15 3.24 1.77 30.37 10.13 81.17 8.70 27.51 76.31 12.40 8.67 3.01 4.25 23.42 9.87 11.68 37.16 12.75 10.96 15.77 c 0.16 0.35 0.36 0.51 0.46 1.47 0.59 8.02 2.94 0.88 0.79 0.58 0.49 1.38 1.13 1.81 3.84 0.48 1.08 2.37 0.23 0.32 0.24 0.71 0.41 1.71 1.99 10.71 4.93 2.54 0.86 0.89 0.55 3.74 0.55 1.64 5.51 2.20 4.24 3.26 1014 0.28 1.10 0.40 1.94 41.69 3.14 14.85 33.60 81.51 21.86 5.98 4.75 2.37 0.91 11.01 5.67 47.33 13.92 13.00 6.95 4044 0.66 1.18 0.75 1.64 1.89 46.74 14.09 53.67 7.62 13.81 3.67 2.29 5.07 19.49 7.92 17.47 36.25 15.61 29.27 11.00 80 1.41 3.30 2.50 26.19 13.72 85.57 6.85 22.66 83.92 15.77 13.06 3.01 1.64 27.43 5.00 15.39 41.58 15.19 14.14 11.15 a 0.09 0.36 0.40 0.50 1.06 3.41 0.50 2.69 2.74 1.14 0.77 0.43 0.98 1.21 1.22 1.79 3.39 1.61 4.25 1.67 0.08 0.31 0.37 1.24 1.16 1.72 2.27 7.00 2.37 1.97 1.37 0.29 0.62 1.94 1.07 1.28 2.14 1.92 8.55 0.56 1014 0.24 1.11 0.65 11.33 111.54 7.81 7.99 58.69 57.61 6.35 3.47 1.47 3.36 3.00 4.05 6.16 6.76 5.22 27.41 7.92 4044 0.24 0.59 1.00 4.60 3.98 74.90 8.36 16.86 6.14 2.15 1.53 2.25 2.55 6.16 3.24 3.51 6.92 3.98 22.56 3.16 80 1.05 2.99 1.44 35.26 7.74 9.24 28.85 46.60 12.80 6.49 1.49 3.29 2.53 7.14 5.09 14.87 5.64 5.23 12.26 HC b 0.12 0.45 0.25 1.72 1.15 3.05 0.52 4.21 2.57 0.93 0.97 0.45 0.65 2.21 1.00 1.86 2.95 1.40 4.19 1.74 0.17 0.65 0.32 2.24 1.51 4.48 1.78 8.16 3.88 1.42 1.18 0.58 0.89 2.98 1.23 2.02 3.66 1.90 6.18 2.35 1014 0.40 1.98 1.05 10.35 60.57 6.32 9.92 78.31 40.58 5.52 3.83 1.96 3.29 6.05 3.58 3.88 14.40 6.91 39.54 10.74 4044 0.79 2.69 1.03 7.57 7.72 84.74 5.87 28.30 9.60 4.37 3.62 2.34 2.92 12.85 4.06 7.45 9.60 6.48 23.79 6.93 80 0.86 3.00 1.27 28.62 10.47 8.54 26.38 45.97 9.17 9.76 2.33 3.65 21.28 8.17 10.81 19.95 10.60 16.29 11.74 c 0.14 0.33 0.14 1.70 1.17 2.72 0.19 7.26 0.89 0.94 1.29 0.28 1.05 1.87 1.16 1.78 2.92 0.49 3.42 0.94 0.16 0.63 0.20 0.93 1.15 3.56 2.02 8.21 1.80 0.95 0.99 0.42 1.39 1.49 1.56 2.09 5.06 0.48 8.55 1.00 1014 0.32 1.30 0.55 3.63 55.39 3.63 14.91 64.18 31.70 4.77 5.43 0.96 4.99 2.35 5.54 2.34 12.69 2.21 28.55 6.79 4044 0.52 1.11 0.57 3.72 6.11 81.54 5.15 32.21 5.97 3.55 4.36 1.54 2.45 13.52 1.17 10.34 6.37 5.61 31.35 3.75 80 0.72 3.25 1.37 20.59 11.15 5.53 14.91 42.31 8.13 11.56 1.50 2.48 7.20 6.59 14.99 21.90 9.83 20.34 10.64 a 2003pp.800805 4 bhc80 3 3.3c 4 1 2 3 4 5 6 7 8 9 10 1112 13 1415 16 17 18 19 20 29
9920109 HC V h COV 1 COV 2 HP SHP JK1 JK2 RG1 RG2 0 17244 24752 20778815 79.33 1.19 16.14 2.09 1.03 1.19 1.02 1.17 0.92 1 15478 22235 18681895 79.31 1.26 17.91 2.42 1.17 1.26 1.07 1.17 0.96 2 12284 17688 14765859 78.88 1.41 22.40 2.83 1.48 1.41 1.20 1.40 0.45 3 8709 12589 10475878 78.73 1.66 30.70 4.22 1.86 1.67 1.41 1.33 0.95 4 5309 7675 6331961 78.27 2.07 47.17 6.47 2.61 2.07 1.76 1.76 0.78 5 2666 3874 3227908 77.56 3.00 95.02 14.30 5.94 3.01 2.52 2.05 2.73 6 2558 3726 3118343 77.89 3.07 99.50 15.53 6.21 3.08 2.57 2.05 2.66 7 2359 3439 2885721 78.20 3.15 106.62 16.10 6.63 3.16 2.65 2.29 2.98 8 2085 3025 2528570 78.95 3.38 125.30 19.90 6.63 3.42 2.85 2.11 3.10 9 1741 2533 2107352 79.13 3.73 148.48 24.90 9.92 3.74 3.09 3.11 3.34 10 1389 2041 1713581 80.58 4.18 184.37 35.68 13.89 4.18 3.37 4.20 3.38 3.52 4.60 11 1060 1557 1298632 81.31 4.86 251.25 48.78 20.46 4.89 3.92 4.92 3.93 3.72 6.53 12 744 1086 886209 79.51 4.99 278.23 43.92 13.49 5.00 4.20 5.02 4.22 5.30 5.46 13 516 765 613903 77.97 6.09 404.22 60.67 19.22 6.12 5.17 6.17 5.20 4.73 7.19 14 337 525 413201 77.33 6.73 521.90 46.06 31.39 6.77 5.92 6.85 5.97 5.43 7.72 15 209 332 279925 80.64 7.90 794.48 62.94 47.47 8.06 7.08 8.21 7.19 5.37 6.13 16 118 199 161931 76.25 10.03 1085.74 95.56 93.10 11.37 9.97 11.84 10.25 8.33 25.03 17 68 104 88742 66.72 11.11 1023.13 141.72 33.21 14.04 13.05 15.25 13.87 14.00 9.59 18 29 43 34751 61.72 24.46 2357.88 1653.81 15.41 20.19 16.24 24.75 17.91 30.78 13.79 1 5 90 61896 5 HCV h COV 1 COV 2 3.3HPSHPRG1JK14 RG2RG1 JK21 2 JK1JK2 10 30
n1 n2 Cor1 Cor2 Cor1 Cor2 0 0.74 80.41 0.01 79.30 58.28 0.48 0.53 0.28 0.30 4088 4112 1 0.78 80.66 0.01 79.31 58.32 0.48 0.54 0.15 0.31 3667 3698 2 0.88 80.19 0.01 78.88 58.27 0.48 0.55 0.28 0.31 2900 2926 3 1.05 80.70 0.02 78.68 58.61 0.49 0.51 0.30 0.31 2087 2065 4 1.34 80.24 0.02 78.17 57.86 0.47 0.48 0.32 0.33 1255 1278 5 1.89 80.10 0.03 77.46 57.83 0.50 0.49 0.37 0.33 634 661 6 1.91 80.58 0.03 77.77 57.65 0.49 0.50 0.38 0.33 610 639 7 2.00 80.94 0.03 78.01 57.77 0.48 0.48 0.39 0.32 557 597 8 2.12 80.50 0.03 78.68 57.50 0.49 0.50 0.34 0.32 481 525 9 2.33 80.67 0.04 78.84 57.32 0.51 0.49 0.38 0.31 401 440 10 2.63 81.89 0.04 80.29 57.06 0.48 0.50 0.40 0.35 322 348 11 3.02 82.65 0.05 80.94 57.11 0.66 0.52 0.44 0.37 250 266 12 3.58 83.55 0.05 79.42 55.20 0.64 0.44 0.47 0.30 175 191 13 4.31 80.51 0.07 78.11 57.31 0.60 0.50 0.51 0.37 121 133 14 4.71 79.40 0.08 77.21 53.18 0.63 0.56 0.21 0.50 82 91 15 5.49 82.41 0.09 80.18 50.32 0.66 0.60 0.06 0.45 54 61 16 7.42 76.28 0.12 73.83 51.06 0.66 0.60 0.03 0.46 31 40 17 10.10 65.63 0.16 62.77 49.15 0.72 0.62 0.51 0.12 12 20 18 18.46 57.56 0.28 60.16 52.74 0.87 0.60 0.72 0.27 3 8 SPSS MW MW 15 Cor1 Cor2 Cor1Cor2 n1n2 31
9920109 1 2 3 MP MW 2 MW MP 4 MW 5 8 2 1 2 6 20092005 Cochran, W.G.1977StataCorp.2009 7 2003 8 1 PSU 2 SSU 20022003 / PSU PSU PSU 2.3SSU PSU 0.004 0.004 0.007 0.007 0.010 0.010 0.013 0.013 0.016 0.016 0.019 0.019 3 12 10 8 5 5 4 9 2001 4 MP 10 Kurihara, Y.2010 hij 32 m 1 ˆV ˆ y ˆ h 2 h + 2 i h j i hij hij hij h + m ˆ h 1 Nh + 11 2005pp.115117 2009pp.139145StataCorp.2009pp.155160 12 7 2 1
Eurostat20092010 1 1 1 13 HC 45 14 15 MW 16 1 SE Freq 2 ˆ v v VFreq ˆ + 1 1 whij v 2 SEFreq ˆ + hij hij ˆ + v 1 Nˆ hij hij h+ ˆV ˆ 1 1 Freq + 2 SEFreq ˆ + hijwhij hij ˆ + ˆ ˆ hijwhij N+ N+ 1 + ˆ MW 2 17 Wolter, K.M.2007pp.2227 18 Wolter, K.M.2007pp.152153 19 MW MW 20 21 2 22 MW 2 33
9920109 1 2010 2 No. 39pp.6788 2 2002 12 3 2003 13 1 1 4 2005 13 62pp.2370. 5 2009 6 1998 7 2005 8 2010HETUS2008 No. 107pp.2123 9 Cochran, W. G.1977, Sampling Techniques, Third Edition, John Wiley & Sons. 10Eurostat2009, Harmonised European time use surveys : 2008 guidelines, pp.1618, eurostat Methodologies and Working papers. 11Wolter, K.M.2007, Introduction to Variance Estimation Second Edition, Springer. 12Kurihara, Y.2010, Estimation of Weekday Averages and Their Variance with The Resampled Data from The Survey on Time Use and Leisure Activities, The Annual of the Institute of Economic Research Chuo University, No. 41, The Institute of Economic Research Chuo University. 13Patterson, H.D.1950, Sampling on Successive Occasions with partial replacement of Units, Journal of the Royal Statistical Society Series B Methodological, Vol. 12, pp.241255. 14Skinner, C.J.1989, Analysis of Complex Surveys, ed. C.J. Skinner, D. Holt & T.M.F. Smith, pp.23 58, John Wiley & Sons. 15StataCorp.2009, Stata Survey Data Reference Manual Release 11, pp.163164. 34
Estimation of Sampling Errors in Measures of the Average of Weekday Using Anonymized Microdata from the Japanese Survey on Time Use and Leisure Activities Yukiko KURIHARA Graduate school of economics, Chuo University ; ebaku24@gmail.com This paper theoretically studies the estimator of the average of weekday and its variance by utilizing anonymized microdata from the Japanese Survey on Time Use and Leisure Activities. It also investigates efficient and practical data handling by calculating the adjusted weight of the pooled data over a weekday. To examine the basic characteristics of weekday activities on the basis of time use data, we use conventional measures to estimate the average of weekday, such as mean statistics by days. However, there are several issues to be noted for the calculations. First, we need to assume that the household clusters were randomly sampled, because the original sampling information is not available, although we are aware that stratified twostage sampling was employed. Second, a customized computing program was required in order to exist covariance caused by the survey method that the households were surveyed over two days. Japanese Survey on Time Use and Leisure Activities, anonymized microdata, fixed samples, sampling error, adjusted weight 35