統計学第99号.indb

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1 ebaku24@gmail.com

2 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 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

3 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 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

4 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 h 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 kg h fkgfkgfh B h r kg kg pp m h m kg 8 hij w hkgi Household ClusterHC

5 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' MW HC HC HC HC 総数男男 (10-14 歳 ) 男 (40-44 歳 ) 男 (80 歳 -) 1 HC

6 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 HC HC 2 HC

7 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 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 k ˆV ˆ RG k ˆkˆ 4 1 SE V ˆ ˆ RG / JKThe deleteone jackknife 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 HC m h 20 m h 26

8 (%) ( 世帯数 ) HC RG1 HP RG2 SHP ウェイト無 JK ( 世帯数 ) Cor1 * Cor2 * Cor1 * +Cor2 * 21 HC 3.3HP 4.1SHP HCHPSHPRG1RG2 JK1 2 RG1 RG HP HC SHP HC HP SHP HC Cor1 0.6 Cor2 100 SHP HC HP 27

9 HP SHP HP HP

10 a HC b c a HC b c a 2003pp bhc c

11 HC V h COV 1 COV 2 HP SHP JK1 JK2 RG1 RG HCV h COV 1 COV 2 3.3HPSHPRG1JK14 RG2RG1 JK21 2 JK1JK

12 n1 n2 Cor1 Cor2 Cor1 Cor SPSS MW MW 15 Cor1 Cor2 Cor1Cor2 n1n2 31

13 MP MW 2 MW MP 4 MW Cochran, W.G.1977StataCorp PSU 2 SSU / PSU PSU PSU 2.3SSU PSU 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 pp pp StataCorp.2009pp

14 Eurostat HC MW 16 1 SE Freq 2 ˆ v v VFreq ˆ 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 Wolter, K.M.2007pp MW MW MW 2 33

15 No. 39pp pp HETUS2008 No. 107pp 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 Skinner, 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

16 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

先端社会研究　★５★号／４．山崎

先端社会研究　★５★号／４．山崎 71 72 5 1 2005 7 8 47 14 2,379 2,440 1 2 3 2 73 4 3 1 4 1 5 1 5 8 3 2002 79 232 2 1999 249 265 74 5 3 5. 1 1 3. 1 1 2004 4. 1 23 2 75 52 5,000 2 500 250 250 125 3 1995 1998 76 5 1 2 1 100 2004 4 100 200