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題名 抽樣調查中關於缺失資料之各種補齊法性質之研究 作者 楊淑蘭 貢獻者 金建輝
楊淑蘭日期 1989 上傳時間 4-五月-2016 14:24:05 (UTC+8) 摘要 論文摘要 由於時代的急速變遷，人們所面臨的問題日趨複雜。在有限的人力與財力限制之下，欲對目標母體(target population) ，作一詳細的調查與研究通常是不可能的，因此如何藉由抽樣方法從母體中抽取具有代表性的樣本是重要的。在抽樣調查的過程中我們常常發現樣本回收率沒有原來預期的高，若我們只用回收的樣本去做資料分析，常常使我們作成的結果有偏誤(biased) 。本文的目的即在針對此一問題，做一深入的研究探討。 在日常生活中經常會遇到所欲研究變數y與其另一輔助變數x有某種線性關係存在。例如農作物產量與種植面積、 家庭收入與家庭支出、1980 年全市人口總數與1970 年全市人口總數等。為方便研究起見，首先假設一簡單的線性迴歸模式： Y 1 =βX 1 +ε1 ε1~i.i.d.N ( 0，σ2 ) 在上式中，若(X1，YI ) i=l , 2 , ......n 為一完整的資料集，即n個隨機樣本(X1 , Y1) 皆無缺失值，則β 與σ2 的最小平方估計式可以很快求出，現在假設y值有部份缺失值，則必須想辦法把缺失的y值補齊，才能進一步研究β 與σ2 的性質，本文即針對下列六種插補法， (a)平均插補法(10) 、(b)隨機插補法(R 0)、(c)分層平均插補法（MC）、(d)分層隨機插補法(RC) 、(e)簡單迴歸插補法(R G)及(f)隨機迴歸插補法(RRS，RRN)，根據所建立的模式，運用各種不同的插補法將缺失值予以補齊後，對模式結果作理論的探討，並對各種插補法作綜合分析比較。最後利用其理論結果，配合1986 年美國零售交易普查資料作實證研究，並分析其實證結果。 參考文獻 參考文獻 [1] Afifi, A. A. and Elashoff, R. M. (1966): " Missing Observations in Multivariate Statistics I. Review of the Literature", Journal of the American Statistical Association, 61(1966), pp. 595-604. [2] Bailar, B. A. ,and Bailey L. and Corby C. (1978): " a Comparison of Some Adjustment and Weighting Procedures for Survey Data", Survey Sampling and Measurement , pp. 175-198, Hew York : Academic Press. [3] Dempster, A. P. , Laird, H. M. and Rubin, D. B. (1977) " Maximum Likelihood From Incomplete Data Via the EM algorithm" , J. R. Statist. Soc. , B. 39 , PP. 1-38. [4] Freedman, D. A. (1986): " A Case Study in Nonresponse: Plaintiff vs. California State Board of Equalization " , Journal of Business & Economic Statistics, January 1986, Vol. 4, NO 1 , pp. 123-124. [5] Hansen, M. H. and Hurwitz, W. N. (1946):" The Problem of Non-response in Sample Surveys", Journal of the American Statistician 41, PP. 517-529. [6] Herzog, T. N. and Lancaster, C. (1980) "Multiple Imputation of Individual Social Security Amounts, Part I ." , Proc. Sect. Survey Res. Meth. , Amer. Statist. Ass. ,1980, PP. 398-403. [7] Herzog, T. N. (1980): " Multiple Imputation of Individual Social Security Amounts, PartⅡ. ", Proc. Sect, Survey Res, Meth.,Amer,Statist,Ass. 1980,pp.404-407. [8] Huang Elizabeth T. (1984) "An Imputation Study for the Monthly Retail Trade Survey" , Proceedings of the Section on Survey Research Methods, American Statistical Association, pp. 610-615. [9] Huang Elizabeth T. (1986) "Comparison of the Different Imputation Procedures in the Monthly Retail Survey". Proceedings of the Section on Survey Research Methods. American Statistical Association. pp. 310-315. [10] Jinn J. H. and Sedransk J.:"Efeect on Secondary Data Analysis of Different Imputation Methods" , unpublished thesis. state university of New York at Albany, Dept. of Math. & Statistics. pp. 1-46. [11] Kaiser J. (1983):"The Effectiveness of Hot-Deck Procedures 1n Small Samples". Proceedings of the Section on Survey Research Methods. American Statistical Association. PP. 523-528. [12] Kalton. G. , Kasprzyk, D. and Santos. R. (1981): "Issues of Nonresponse and Imputation in the Survey of Income and Program Participation", Current Topics in Survey Sampling, pp. 455-480,New York: Academic Press. [13] Kalton, G. and Kasprzyk, D. (1982) "Imputing for Missing Survey Response", Proe. Sect. Survey Res. Meth., Amer. Statist. Assoc., pp. 22-33. [l4] Kalton, G.and Kasprzyk. D. (1986) "The Treatment of Hissing Survey Data" Survey Methodology,June 1986. Vol. 12, NO.1. pp. 1-16,Statistics Canada. [15] Kalton, G. and Kish, L. (1981) "Two Effect Random Imputation Procedures",Proc. Sect. Survey Res. Meth., Amer. Statist. Assoc.,pp. 146-151. [16] Kott, P.S. (1987) :"Nonresponse in a Periodic Sample Survey" , Journal of Business & Economic Statistics; April 1987, Vol 5, No.2, pp. 287-293. [17] Kovar, M. G. (1984) "Imputation in Small Surveys: The Effect on Small Domain Estimates", Proceeding of the Section on Survey Research Methods, American Statistical Association, PP. 628-633. [18] Lepkowski, J. M. , Stehouwer S. A. and Landis, J. R. (1983) : " Strategies for the Analysis of Imputed Data In a Sample Survey", Proceeding of the Section on Survey Research Methods, American Statistical Association, pp. 622-627. [19] Lievesley Denise (1983) :" Reducing Unit Nonresponse in Interview Surveys", Proceeding of the Section on Survey Research Methods, American Statistical Association, pp. 295-299. [20] Lusk, E. J. and Pagell,? R. A. (1985) :" Sampling and Non response : a Method for Deciding upon a Follow Up", Proceeding of the Section on Survey Research Methods, American Statistical Association, PP. 266-268. [21] Michaud S. (1986): "Weighting VS Imputation: a Simulation Study", Proceeding of the Section on Survey Research Methods, American Statistical Association, PP. 316-320. [22] Moser,C.A.and Kalton G.(1971):Survey Methods in Social Investigation, 2nd ed. London, Heinemann Educational, 1971. [23] Oh, H. L. and Scheuren F. (1980) " Estimating the Variance Impact of Missing CPS income deta" Proc. Sect. Survey Res. Meth. Amer. Statist. Ass. 1980 pp. 408-415. [24] Platek, R. , Singh, M. P. and Tremblay, V. (1978):" Adjustment for Nonresponse in Surveys "Sampling and Measurement, pp. 157-174, Academic Press. Survey New York: [25] Sande, I. G. (1979a) "A Personal View of Hot Deck Imputation Procedures " Survey Methodology, 5. pp. 238-258. [26] Sande. I. G. (1982): "Imputation in Surveys Coping With Reality" The American Statistician, August 1982. Vol. 36. Ho. 3. part 1. pp. 145-152. [27] Santos. R. L. (1981b): "Effects of Imputation on Regression Coefficients" , Proc. Sect. Survey Res. Meth. Amer. Statist. Ass . 1981. pp. 140-145. [28] Shih Wen-Fu P. (1983): "Nonresponses to Income Questions in Telephone Surveys", Proceeding of the Section on Survey Research Methods. American Statistical Association. pp. 283-288. [29] Scheiber , S. J. (1978): " A Comparison of Three Alternative Techniques for Allocating Unreported Social Security Income on the Survey of the Low Income Aged and Disabled", Proc. Sect. survey Res. Meth, Amer. Statist. Ass., 1978, pp.212-218. [30] Welniak . E. J. and Coder. J. F. (1980) "A Measure of the bias in the March CPS earnings Imputation system”, Proc. Sect, Survey Res ,Meth., Amer, Statist. Ass, 1980, pp.421-425 描述 碩士
國立政治大學
統計學系資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002005728 資料類型 thesis dc.contributor.advisor 金建輝 zh_TW dc.contributor.author (作者) 楊淑蘭 zh_TW dc.creator (作者) 楊淑蘭 zh_TW dc.date (日期) 1989 en_US dc.date.accessioned 4-五月-2016 14:24:05 (UTC+8) - dc.date.available 4-五月-2016 14:24:05 (UTC+8) - dc.date.issued (上傳時間) 4-五月-2016 14:24:05 (UTC+8) - dc.identifier (其他 識別碼) B2002005728 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/90494 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description.abstract (摘要) 論文摘要 由於時代的急速變遷，人們所面臨的問題日趨複雜。在有限的人力與財力限制之下，欲對目標母體(target population) ，作一詳細的調查與研究通常是不可能的，因此如何藉由抽樣方法從母體中抽取具有代表性的樣本是重要的。在抽樣調查的過程中我們常常發現樣本回收率沒有原來預期的高，若我們只用回收的樣本去做資料分析，常常使我們作成的結果有偏誤(biased) 。本文的目的即在針對此一問題，做一深入的研究探討。 在日常生活中經常會遇到所欲研究變數y與其另一輔助變數x有某種線性關係存在。例如農作物產量與種植面積、 家庭收入與家庭支出、1980 年全市人口總數與1970 年全市人口總數等。為方便研究起見，首先假設一簡單的線性迴歸模式： Y 1 =βX 1 +ε1 ε1~i.i.d.N ( 0，σ2 ) 在上式中，若(X1，YI ) i=l , 2 , ......n 為一完整的資料集，即n個隨機樣本(X1 , Y1) 皆無缺失值，則β 與σ2 的最小平方估計式可以很快求出，現在假設y值有部份缺失值，則必須想辦法把缺失的y值補齊，才能進一步研究β 與σ2 的性質，本文即針對下列六種插補法， (a)平均插補法(10) 、(b)隨機插補法(R 0)、(c)分層平均插補法（MC）、(d)分層隨機插補法(RC) 、(e)簡單迴歸插補法(R G)及(f)隨機迴歸插補法(RRS，RRN)，根據所建立的模式，運用各種不同的插補法將缺失值予以補齊後，對模式結果作理論的探討，並對各種插補法作綜合分析比較。最後利用其理論結果，配合1986 年美國零售交易普查資料作實證研究，並分析其實證結果。 zh_TW dc.description.tableofcontents 目錄 第零章 論文結構…… 1 第一章 緒論 第一節 研究動機與目的……2 第三節 文獻回顧……5 第二章 相關名詞的定義 第一節 基本定義……15 第二節 研究方法……19 第三節 分析方法……23 第四節 研究限制……28 第三章 各種插補法(IMPUTATION) 性質的分析 第一節 平均插補法 Mean Imputation Overall……29 第二節 隨機插補法 Random Imputation Overall……35 第三節 分層平均插補法 Mean Imputation Within Cells……42 第四節 分層隨機插補法 Random Imputation Within Cells……47 第五節 簡單迴歸插補法 Simple Regression Prediction Imputation……55 第六節 隨機迴歸插補法 Random Regression Imputation……59 第七節 綜合比較分析……72 第四章 實証分析 第一節 資料來源……75 第二節 實証結果……79 第五章 結論……98 附錄……101 參考文獻……125 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002005728 en_US dc.title (題名) 抽樣調查中關於缺失資料之各種補齊法性質之研究 zh_TW dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 參考文獻 [1] Afifi, A. A. and Elashoff, R. M. (1966): " Missing Observations in Multivariate Statistics I. Review of the Literature", Journal of the American Statistical Association, 61(1966), pp. 595-604. [2] Bailar, B. A. ,and Bailey L. and Corby C. (1978): " a Comparison of Some Adjustment and Weighting Procedures for Survey Data", Survey Sampling and Measurement , pp. 175-198, Hew York : Academic Press. [3] Dempster, A. P. , Laird, H. M. and Rubin, D. B. (1977) " Maximum Likelihood From Incomplete Data Via the EM algorithm" , J. R. Statist. Soc. , B. 39 , PP. 1-38. [4] Freedman, D. A. (1986): " A Case Study in Nonresponse: Plaintiff vs. California State Board of Equalization " , Journal of Business & Economic Statistics, January 1986, Vol. 4, NO 1 , pp. 123-124. [5] Hansen, M. H. and Hurwitz, W. N. (1946):" The Problem of Non-response in Sample Surveys", Journal of the American Statistician 41, PP. 517-529. [6] Herzog, T. N. and Lancaster, C. (1980) "Multiple Imputation of Individual Social Security Amounts, Part I ." , Proc. Sect. Survey Res. Meth. , Amer. Statist. Ass. ,1980, PP. 398-403. [7] Herzog, T. N. (1980): " Multiple Imputation of Individual Social Security Amounts, PartⅡ. ", Proc. Sect, Survey Res, Meth.,Amer,Statist,Ass. 1980,pp.404-407. [8] Huang Elizabeth T. (1984) "An Imputation Study for the Monthly Retail Trade Survey" , Proceedings of the Section on Survey Research Methods, American Statistical Association, pp. 610-615. [9] Huang Elizabeth T. (1986) "Comparison of the Different Imputation Procedures in the Monthly Retail Survey". Proceedings of the Section on Survey Research Methods. American Statistical Association. pp. 310-315. [10] Jinn J. H. and Sedransk J.:"Efeect on Secondary Data Analysis of Different Imputation Methods" , unpublished thesis. state university of New York at Albany, Dept. of Math. & Statistics. pp. 1-46. [11] Kaiser J. (1983):"The Effectiveness of Hot-Deck Procedures 1n Small Samples". Proceedings of the Section on Survey Research Methods. American Statistical Association. PP. 523-528. [12] Kalton. G. , Kasprzyk, D. and Santos. R. (1981): "Issues of Nonresponse and Imputation in the Survey of Income and Program Participation", Current Topics in Survey Sampling, pp. 455-480,New York: Academic Press. [13] Kalton, G. and Kasprzyk, D. (1982) "Imputing for Missing Survey Response", Proe. Sect. Survey Res. Meth., Amer. Statist. Assoc., pp. 22-33. [l4] Kalton, G.and Kasprzyk. D. (1986) "The Treatment of Hissing Survey Data" Survey Methodology,June 1986. Vol. 12, NO.1. pp. 1-16,Statistics Canada. [15] Kalton, G. and Kish, L. (1981) "Two Effect Random Imputation Procedures",Proc. Sect. Survey Res. Meth., Amer. Statist. Assoc.,pp. 146-151. [16] Kott, P.S. (1987) :"Nonresponse in a Periodic Sample Survey" , Journal of Business & Economic Statistics; April 1987, Vol 5, No.2, pp. 287-293. [17] Kovar, M. G. (1984) "Imputation in Small Surveys: The Effect on Small Domain Estimates", Proceeding of the Section on Survey Research Methods, American Statistical Association, PP. 628-633. [18] Lepkowski, J. M. , Stehouwer S. A. and Landis, J. R. (1983) : " Strategies for the Analysis of Imputed Data In a Sample Survey", Proceeding of the Section on Survey Research Methods, American Statistical Association, pp. 622-627. [19] Lievesley Denise (1983) :" Reducing Unit Nonresponse in Interview Surveys", Proceeding of the Section on Survey Research Methods, American Statistical Association, pp. 295-299. [20] Lusk, E. J. and Pagell,? R. A. (1985) :" Sampling and Non response : a Method for Deciding upon a Follow Up", Proceeding of the Section on Survey Research Methods, American Statistical Association, PP. 266-268. [21] Michaud S. (1986): "Weighting VS Imputation: a Simulation Study", Proceeding of the Section on Survey Research Methods, American Statistical Association, PP. 316-320. [22] Moser,C.A.and Kalton G.(1971):Survey Methods in Social Investigation, 2nd ed. London, Heinemann Educational, 1971. [23] Oh, H. L. and Scheuren F. (1980) " Estimating the Variance Impact of Missing CPS income deta" Proc. Sect. Survey Res. Meth. Amer. Statist. Ass. 1980 pp. 408-415. [24] Platek, R. , Singh, M. P. and Tremblay, V. (1978):" Adjustment for Nonresponse in Surveys "Sampling and Measurement, pp. 157-174, Academic Press. Survey New York: [25] Sande, I. G. (1979a) "A Personal View of Hot Deck Imputation Procedures " Survey Methodology, 5. pp. 238-258. [26] Sande. I. G. (1982): "Imputation in Surveys Coping With Reality" The American Statistician, August 1982. Vol. 36. Ho. 3. part 1. pp. 145-152. [27] Santos. R. L. (1981b): "Effects of Imputation on Regression Coefficients" , Proc. Sect. Survey Res. Meth. Amer. Statist. Ass . 1981. pp. 140-145. [28] Shih Wen-Fu P. (1983): "Nonresponses to Income Questions in Telephone Surveys", Proceeding of the Section on Survey Research Methods. American Statistical Association. pp. 283-288. [29] Scheiber , S. J. (1978): " A Comparison of Three Alternative Techniques for Allocating Unreported Social Security Income on the Survey of the Low Income Aged and Disabled", Proc. Sect. survey Res. Meth, Amer. Statist. Ass., 1978, pp.212-218. [30] Welniak . E. J. and Coder. J. F. (1980) "A Measure of the bias in the March CPS earnings Imputation system”, Proc. Sect, Survey Res ,Meth., Amer, Statist. Ass, 1980, pp.421-425 zh_TW
