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題名 有限群體分類資料之適合度及獨立性檢定之研究 作者 邱瑞滿 貢獻者 魏應澤
邱瑞滿日期 1984 上傳時間 14-十一月-2016 14:56:53 (UTC+8) 摘要 第一章 緒論1 第一節 研究動機1 第二節 研究目的1第三節 本文結構2 第二章 適合度檢定3 第一節 XG2統計式3 第二節 XW2統計式7 第三節 漸近理論10 第四節 設計效果38 第五節 幾種抽樣設計之適合度檢定41 第六節 特殊集體抽樣模式下之適合度檢定59 第七節 XG2之修正65 第八節 抽樣設計對XG2之影響73第三章 二向關聯表變數間的獨立性檢定81 第一節 X2(h)之漸近分布81第二節 XI2之漸近分布88 第三節 特殊集體抽樣模式下之獨立性檢定90 第四節 XI2之修正99 第五節 抽樣設計對XI2之影響105 第四章 多向關聯表變數間的獨立性檢定111第一節 log-linear模式111第二節 X2之漸近分布116第三節 XW2之漸近分布124第四節 X2之修正130第五節 抽樣設計對 X2之影響143第五章 結論149參考資料153附錄：一、多變量δ法159 二、變方之推算法-線性化法、摺刀法及BRR法161 三、證明 H△H`= △r × △C 169 四、Bishop et al (1975) , P. 510之正則條件175 參考文獻 1. Altham, P. A. E. (1976),“Discrete Variable Analysis for Individuals Grouped Into Families,” Biometrika, 63, 263-269.2. Anderson, T. W. , and Das Gupta, S. (1963), “Some Inequalities on Characteristic Roots of Matrices,” Biometrika , 50, 522-524.3. Bhapkar ,V. P. (1966), “A Note on the Equivalence of Two Test Criteria for Hypotheses in Categorical Data, ” Journal of the American Statistical Association, 61 , 228-235.4. Bishop, Y. M. M. , Fienberg, S. E. , and Holland, P. W. (1975), Discrete Multivariate Analysis : Theory and Practice, Cambridge, Mass. : MIT Press.5. Brier, S . S. (1980), “Analysis of contingency tables under cluster Sampling,”Biometrika, 67 , 3 , 591-5966. Cochran G. W. (1977), Sampling Techniques, 3rd ed. New York : John Wiley & Sons, Inc.7. Cohen, J. E. (1976), “The Distribution of the Chi-Squared Statistic Under Cluster Sampling From Contingency Tables, ” Journal of the American Statistical Association, 71 , 665-670.8. Fellegi, I. P. (1980), “ Approximate Tests of Independence and Goodness of Fit Based on Stratified Multistage Samples, ” Journal of the American Statistical Association, 75 , 261-268.9. Fuller, W. A. (1975), Regression Analysis for Sample Surveys,” Sankyã, Ser. C, 37 , 117-132.10. Goodman L ,A. (1978), Analyzing Qualitative/ Categorical Data, Cambridge, Mass.: Abt Associates Inc.11. Grabill A.F. (1969), Introduction to Matrices with Applications in Statistics, 1st ed, 台北淡江書局12. Hajek, J. (1964), “Asymptotic Theory of Rejective Sampling With Varying Probabilities From a Finite Population, ”Annals of Mathematical Statistics, 35 , 1491-1523.13. Hidiroglou, M, A. and Rao, J. N. K,(1981), “ Chi-square Tests for the Analysis of Categorical Data From the Canada Health Survey,” Statistics Canada and Carleton University, Ottawa, Canada.14. Holt , D. , Scott , A. J. ,and Ewings, P.O. (1980), Chi-squared Tests With Survey Data, ” Journal of the Royal Statistical Society, Ser. A,143, 302-320.15. Johnson, and N. L., and Kotz, S. (1970), Continuous Univariate Distributions, Boston: Houghton Mifflin.16. Kish, L. , and Frankel, M. R. (1974), “ Inference From Complex Samples, ” Journal of the Royal Statistical Society , Ser. B, 36, 1-37.17. Koch, G. G. , Freeman, D. H. , JR., and Freeman, J. L .(1975), “ Strategies in the Multivariate Analysis of Data From Complex Surveys, ” International Statistical Review, 43 , 59-78.18. Krewski D., and Rao, J. N. K (1978), “ Inference from Stratified Samples I : Large Sample Properties of the Linearization, Jackknife and Balanced Repeated Replication Methods, ” Carleton Math. Ser. No. 155, Carleton University, Ottawa, Dept. of Mathematics.19. Madow, W. G.(1948), “ On the Limiting Distributions of Estimates Based on Samples From Finite Universes, ” Annals of Mathematical Statistics, 19 , 535-545.20. Mosimann, J. E. (1962), “On the Compound Multinomial Distribution, the Multivariate β- distribution, and Correlation Among Proportions, Biometrika, 49 , 65-82.21. Nathan, G. (1975), “ Tests of Independence in Contingency Tables From Stratified Proportional Samples, ”Sankbyã ,Ser. C, 37 , 77-87.22. Rao, J. N. K. and Scott, A. J. (1979), “ Chi-Squared Tests for Analysis of Categorical Data From Complex Surveys, ” Proceedings of the American Statistical Association, Section on Survey Research Methods, 58-66.23. Rao, J. N. K. and Scott, A. J. (1981), “ The Analysis of Categorical Data from Complex Sample Surveys: Chi-squared Tests for Goodness of Fit and Independence in Two-Way Tables, ” Journal of the American Statistical Association , 76 , 221-230.24. Rao, J. N. K and Scott, A. J .(1983), “On Chi-Square Tests for Multiway Contingency Tables with Cell Proportions Estimated From Survey Data, ” Carleton Math. Ser. No. 199 , Carleton University, Ottawa, Dept. of Mathematics.25. Rosen, B. (1972), “ Asymptotic Theory for Successive Sampling With Varying Probabilities Without Replacement, I and II, ” Annals of Mathematical Statistics, 43 , 373-397.26. Satterthwaite , F. E. (1946), “ An Approximate Distribution of Estimates of Variance Components, ” Biometrics, 2 , 110-114.27. Seber, G. A . F (1977), Linear Regression Analysis, 台北華泰書局.28. Shuster, J. J. and Dowing.D. J. (1976), “ Two-Way Contingency Tables for Complex Sampling Schemes , ” Biometrika, 63 , 271-276.29. Solomon, H. , and Stephens, M.A.(1977), “Distribution of a Sum of Weighted Chi-Square Variables , ” Journal of the American Statistical Association , 72 , 881-885.30. Stroud, T. W. F.(1971), “On Obtaining Large-Sample Tests From Asymptotically Normal Estimates , ” Annals of Mathematical Statistics , 42 , 1412-1424.31.Von Bahr , B. (1972), “ On Sampling From a Finite Set of Indepedent Random Variables , “ Zeitschrift für Wahrs-cheinlichkeitstheorie and Verwandte Gebiete, 24 , 279-286.32.魏應澤編著，抽樣理論及其應用，自印，民國六十四年九月、再版。 關聯 國立政治大學
統計研究所
碩士
72資料類型 thesis dc.contributor.advisor 魏應澤 dc.contributor.author (作者) 邱瑞滿 dc.creator (作者) 邱瑞滿 zh_TW dc.date (日期) 1984 dc.date.accessioned 14-十一月-2016 14:56:53 (UTC+8) - dc.date.available 14-十一月-2016 14:56:53 (UTC+8) - dc.date.issued (上傳時間) 14-十一月-2016 14:56:53 (UTC+8) - dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/103906 - dc.description.abstract (摘要) 第一章 緒論1 第一節 研究動機1 第二節 研究目的1第三節 本文結構2 第二章 適合度檢定3 第一節 XG2統計式3 第二節 XW2統計式7 第三節 漸近理論10 第四節 設計效果38 第五節 幾種抽樣設計之適合度檢定41 第六節 特殊集體抽樣模式下之適合度檢定59 第七節 XG2之修正65 第八節 抽樣設計對XG2之影響73第三章 二向關聯表變數間的獨立性檢定81 第一節 X2(h)之漸近分布81第二節 XI2之漸近分布88 第三節 特殊集體抽樣模式下之獨立性檢定90 第四節 XI2之修正99 第五節 抽樣設計對XI2之影響105 第四章 多向關聯表變數間的獨立性檢定111第一節 log-linear模式111第二節 X2之漸近分布116第三節 XW2之漸近分布124第四節 X2之修正130第五節 抽樣設計對 X2之影響143第五章 結論149參考資料153附錄：一、多變量δ法159 二、變方之推算法-線性化法、摺刀法及BRR法161 三、證明 H△H`= △r × △C 169 四、Bishop et al (1975) , P. 510之正則條件175 dc.format.extent 115 bytes - dc.format.mimetype text/html - dc.relation (關聯) 國立政治大學 dc.relation (關聯) 統計研究所 dc.relation (關聯) 碩士 dc.relation (關聯) 72 dc.title (題名) 有限群體分類資料之適合度及獨立性檢定之研究 zh_TW dc.type (資料類型) thesis dc.relation.reference (參考文獻) 1. Altham, P. A. E. (1976),“Discrete Variable Analysis for Individuals Grouped Into Families,” Biometrika, 63, 263-269.2. Anderson, T. W. , and Das Gupta, S. (1963), “Some Inequalities on Characteristic Roots of Matrices,” Biometrika , 50, 522-524.3. Bhapkar ,V. P. (1966), “A Note on the Equivalence of Two Test Criteria for Hypotheses in Categorical Data, ” Journal of the American Statistical Association, 61 , 228-235.4. Bishop, Y. M. M. , Fienberg, S. E. , and Holland, P. W. (1975), Discrete Multivariate Analysis : Theory and Practice, Cambridge, Mass. : MIT Press.5. Brier, S . S. (1980), “Analysis of contingency tables under cluster Sampling,”Biometrika, 67 , 3 , 591-5966. Cochran G. W. (1977), Sampling Techniques, 3rd ed. New York : John Wiley & Sons, Inc.7. Cohen, J. E. (1976), “The Distribution of the Chi-Squared Statistic Under Cluster Sampling From Contingency Tables, ” Journal of the American Statistical Association, 71 , 665-670.8. Fellegi, I. P. (1980), “ Approximate Tests of Independence and Goodness of Fit Based on Stratified Multistage Samples, ” Journal of the American Statistical Association, 75 , 261-268.9. Fuller, W. A. (1975), Regression Analysis for Sample Surveys,” Sankyã, Ser. C, 37 , 117-132.10. Goodman L ,A. (1978), Analyzing Qualitative/ Categorical Data, Cambridge, Mass.: Abt Associates Inc.11. Grabill A.F. (1969), Introduction to Matrices with Applications in Statistics, 1st ed, 台北淡江書局12. Hajek, J. (1964), “Asymptotic Theory of Rejective Sampling With Varying Probabilities From a Finite Population, ”Annals of Mathematical Statistics, 35 , 1491-1523.13. Hidiroglou, M, A. and Rao, J. N. K,(1981), “ Chi-square Tests for the Analysis of Categorical Data From the Canada Health Survey,” Statistics Canada and Carleton University, Ottawa, Canada.14. Holt , D. , Scott , A. J. ,and Ewings, P.O. (1980), Chi-squared Tests With Survey Data, ” Journal of the Royal Statistical Society, Ser. A,143, 302-320.15. Johnson, and N. L., and Kotz, S. (1970), Continuous Univariate Distributions, Boston: Houghton Mifflin.16. Kish, L. , and Frankel, M. R. (1974), “ Inference From Complex Samples, ” Journal of the Royal Statistical Society , Ser. B, 36, 1-37.17. Koch, G. G. , Freeman, D. H. , JR., and Freeman, J. L .(1975), “ Strategies in the Multivariate Analysis of Data From Complex Surveys, ” International Statistical Review, 43 , 59-78.18. Krewski D., and Rao, J. N. K (1978), “ Inference from Stratified Samples I : Large Sample Properties of the Linearization, Jackknife and Balanced Repeated Replication Methods, ” Carleton Math. Ser. No. 155, Carleton University, Ottawa, Dept. of Mathematics.19. Madow, W. G.(1948), “ On the Limiting Distributions of Estimates Based on Samples From Finite Universes, ” Annals of Mathematical Statistics, 19 , 535-545.20. Mosimann, J. E. (1962), “On the Compound Multinomial Distribution, the Multivariate β- distribution, and Correlation Among Proportions, Biometrika, 49 , 65-82.21. Nathan, G. (1975), “ Tests of Independence in Contingency Tables From Stratified Proportional Samples, ”Sankbyã ,Ser. C, 37 , 77-87.22. Rao, J. N. K. and Scott, A. J. (1979), “ Chi-Squared Tests for Analysis of Categorical Data From Complex Surveys, ” Proceedings of the American Statistical Association, Section on Survey Research Methods, 58-66.23. Rao, J. N. K. and Scott, A. J. (1981), “ The Analysis of Categorical Data from Complex Sample Surveys: Chi-squared Tests for Goodness of Fit and Independence in Two-Way Tables, ” Journal of the American Statistical Association , 76 , 221-230.24. Rao, J. N. K and Scott, A. J .(1983), “On Chi-Square Tests for Multiway Contingency Tables with Cell Proportions Estimated From Survey Data, ” Carleton Math. Ser. No. 199 , Carleton University, Ottawa, Dept. of Mathematics.25. Rosen, B. (1972), “ Asymptotic Theory for Successive Sampling With Varying Probabilities Without Replacement, I and II, ” Annals of Mathematical Statistics, 43 , 373-397.26. Satterthwaite , F. E. (1946), “ An Approximate Distribution of Estimates of Variance Components, ” Biometrics, 2 , 110-114.27. Seber, G. A . F (1977), Linear Regression Analysis, 台北華泰書局.28. Shuster, J. J. and Dowing.D. J. (1976), “ Two-Way Contingency Tables for Complex Sampling Schemes , ” Biometrika, 63 , 271-276.29. Solomon, H. , and Stephens, M.A.(1977), “Distribution of a Sum of Weighted Chi-Square Variables , ” Journal of the American Statistical Association , 72 , 881-885.30. Stroud, T. W. F.(1971), “On Obtaining Large-Sample Tests From Asymptotically Normal Estimates , ” Annals of Mathematical Statistics , 42 , 1412-1424.31.Von Bahr , B. (1972), “ On Sampling From a Finite Set of Indepedent Random Variables , “ Zeitschrift für Wahrs-cheinlichkeitstheorie and Verwandte Gebiete, 24 , 279-286.32.魏應澤編著，抽樣理論及其應用，自印，民國六十四年九月、再版。
