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題名 多變量模擬輸出之統計分析 作者 許淑卿 貢獻者 余千智
許淑卿日期 1987 上傳時間 4-五月-2016 17:12:32 (UTC+8) 摘要 論文提要 本論文所擬探討之對象為多變量統計分配函數模擬（Simulation）之最佳停止法則問題（Optimal Stopping Rule Problem），此類問題之目的在於設法利用盡量少的樣本觀察值來求得哭未知母數（Unknown Parameter）的信賴區間（域）（Confidence Interval）（Confidence Region），而此信賴區間（域）之寬度（Width）即包含機率（Coverage Probability）均已事先指定。 以往研究者對於最佳停止法則問題的研究對象多侷限於單變量統計分配函數，而多變量統計分配函數模擬之最佳停止法則問題，仍尚在研究階段，因此本論文之重點乃在於探討如何求得滿足最佳停止法則之最小樣本數。在此我們以多變量常態分配函數為重心，發展出一個以信賴區域體積大小為設限標準的最佳停止法則，同時亦提供了一組實際模擬結果的數值比較與分析。 參考文獻 參考書目 1. Alan, K & Saxena, K.M. L., " Bounded Length Confidence Interval for a Common Mean ", Commun, Statist.-theor. Meth., 13(17), 2133-2142, (1984) 2. Anderson, T.W., An Introduction to Multivariate Statistical Analysis, 1st ed., Chicherter Brisbane Toronto, Singapore, (1985) 3. Anderson, T.W., "Estimating Linear Restrictions on Regession Co-efficients for Multivariate Normal Distributions", Ann. Math. Statist., 22, 327–351, (1951b) 4. Anscombe, F.J., " Sequential Estimation ", J.R. Statist. Soc. B 15, 1-21, (1953) 5. Atkinson, A.C. & Pearce, M.C., " The Computer Generation of Beta, Gamma and Normal Random Variable ", J. R. Statist.Soc. A 139,431-448, (1976) 6. Basilevsky, A., Applied Matrix Algebra in the Statistical Science, North-Holland, N.Y., (1983) 7. Basu, D., "On Statisticss Independent of a Complete Sufficient Statistic", sankhya, 15, 377-380 8. Chatfield, C. & Collins, A.J., Introduction to Multivariate Analysis, Chapman & Hall, N.Y., (1988) 9. Chew, V., " Confidence, Prediction, and Tolerance Regions for the Multinormal Distribution ", J. Ame. Statist. Assoc. , 605-617, (1966) 10. Chow, Y. S. & Robbins, H., " On the Asymptotic Theory of Fixed-width Sequential Confidence interval for the Mean ", Ann.Math. Statist., 36,457-462, (1965) 11. Constantine, A.G., "Some Non-central Distribution Problems in Multivariate Analysis", Ann. Math. Statist, , 34, 1270-1285, (1963) 12. Constantine, A.G., "The Distribution of Hotelling`s Generalised Too", Ann.Math. Statist. , 37, 215-225, (1966) 13. Farrel, R.H., Techniques of Multivariate Calculation, Springer-Verlag, N.Y., (1976) 14. Fishman, G.S., Principles of Discrete Event Simulation, John Wiley & sons, N.Y., (1981) 15. Ghosh,M. & Mukhopadhyay, N., "Consistency and Asymptotic Efficiency of two-stage and Sequential Procedures", Sankhya, A, 43, 220-227, (1981) 16. Ghosh, M. & Mukhopadhgag, M., "On Two Fundamental Problems of Sequential Estimation", Sankhya, B 38, 203-218, (1976) 17. Ghosh, H. & Mukhopadhyay, N., "Sequential Point Estimation of the Mean when the Distribution is unspecified", Comm. Statist., A, Theory methods, 8, 637-652, (1979) 18. Ghosh, H., Sinha B.K.,& Mukhopadhyay, N., " Multivariate Sequential . Point Estimation ", J.mult analysis, 6, 281-294, (1976) 19. Ghosh, M. & Sen, P.K., " On Two-stage James-stein Estimators ", J. Sequential Analysis, 2, 359-367, (1984) 20. Gleser, L.J., " On the Asymptotic Theory of fixed-size sequential Confidence Bounds for Linear Regression ", Ann.Math. Statist., 36, 463-467, (1965) 21. Hall, P., "Asymptotic Theory of Triple Sampling for Sequential Estimation of a Hean ", Ann. Statist., 9, 1229-1238, (1981) 22. Hayakawa, T., "On the Distribution of a Quadratic form in a Multivariate Normal Sample", Ann. Inst. Statist.Math., 18, 191-210, (1966) 23. John, S., "A Tolerance Region for Hultivariate Normal Distributions", Sankhya, 25, 363-368, (1963) 24. Johnson, R.A. & Wichern, D.W., Applied Multivariate Statistical Analysis, 1st ed., Prentice-Hall, New Jersey, (1982) 25. Khan, R.A., " Sequential Estimation of the Mean Vector of a Multinormal Distribution ", sankhy?, A, 30, 331-334, (1968) 26. Konishi, S., "An Approximation to the Distribution of the Sample Correlation Cofficient", Bometrika, 65, 654-656, (1978a) 27. Krishnaiah, P. KR. & Chang,T.C., "On the Exact Distributions of the Traces of S1 (S1+S2)-1 and S1S2-1", sankhya, s, 34,153-168, (1972) 28. Law, A.M. & Kelton, W.D., Simulation Modeling and Analysis, McGraw-Hill, N.Y. (1982) 29. Lee, Y.S., "Some Results on the Sampling Distribution of the Multivariate Correlation Coefficient", J. Royal Statist.Soc., B, 33, 117-138, (1971b) 30. Loeve, M., Probability Theory I, 4nd ed., Springer-Verlag, N.Y., (1977) 31. Loeve, M., Probability Theory II, 4nd ed., Springer-Verlag, N.Y., (1978) 32. Mallows, C.L., "Latent Vectors of Random Symmetric Matrices", Biometrika, 48, 133-149, (1961) 33. Mood, A.M., "On the Distribution of the Characteristic Roots of Normal Second-Moment Matrices", Ann.Math. Statist., 22, 266-273, (1951) 34. Morgan, B. J.T., Elements of Simulation, 1st ed., Canterbury, U.K., (1986) 35. Muirhead, R.J., Aspects of Multivariate Statistical Theory, John Wiley & Sons, N.Y., (1982) 36. Mukhopadhyay, N., " Fixed-Size Simultaneous Confidence Region for Mean Vector and Dispersion of a Multimormal Dist. ", Calcutta. Statist. Assoc. Bull., 28., 147-152, (1979) 37. Mukhopadhyay, N. & Al-Mousawi, J.S., " Fixed-Size Confidence Region for the Mean vector of a Multinormal Distribution ", Sequential Analysis, 5(2), 139-168, (1986) 38. Nadas, A., " An Extension of a Theorem of Chow and Robbins on Sequential Confidence Intervals for the Mean ", Ann.Math. Statist., 40(2), 667-671, (1967) 39. Nagao, H., "On Some Test Criteria for Covariance Matrix", Ann. Statist., 1, 700-709, (1973a) 40. Pritsker, A.A.B., Introduction to simulation and SLAM II, 2nd ed., John Wiley & Sons, N.Y., (1985) 41. Proschan, F., "Confidence and Tolerance Intervals for the Normal Distribution", J, Ame. Statist. Ass., 48, 550-564, (1953) 42. Ray, W.D., "Sequential Confidence Intervals for the Mean of a Normal Population with Unknown Variance ", J.R. Statist.Soc., B(19), 133-143, (1957) 43. Roy, S.N., Some Aspects of Multivariate Analysis, John Wiley & Sons, N.Y., (1957) 44. Rohatsi, V.K. a. 0` Neill, R.T., " on Sequential Estimation of the Mean Vector of a Multinormal Population ", Ann. Inst. Statist.Math., 25, 321-325, (1973) 45. Seelbinder, B.M., "On Stein’s Two-stage sampling Scheme", Ann.Math. Statist. , 24, 640-649, (1953) 46. Simons, G., "On the Cost of not knowing the variance when Making a fixed width. Confidence Interval for the Mean", Ann.Math. Statist. , 39, 1946-1952, (1968) 47. Siotani, M., "Tolerance Regions for a Multivariate Normal Population", Ann. Inst. Statist.Math., 16, 135-153, (1964) 48. Sinha, B.K. & Mukhopadhyay, N., "Sequential Estimation of a Bivariate Normal Mean Vector ", Sankhya, B, 38, 219-230, (1976) 49. Srivastava, M.S., " on fixed-Width Confidence Bounds for Regression Parameters and Mean Vector ", J.R.Statist.Soc., B(29), 132-140, (1967) 50. Srivastava,M.S.& Khati,C.G., An Introduction to Multivariate Statistical Elsevier North Holland, Inc., (1979) 51. Starr,N., " The Performance of a Sequential Procedure for the Fixed-Width Interval Estimation of the Mean ", Ann.Math.Statist., 37, 36-50, (1966a) 52. Starr,H., " on the Asymptotic Efficiency of a Sequentical Precedure for Estimating the Mean ", Ann.MathiStatist.,37. 1173-1185, (1966b) 53. Starr,N.& Uoodroofe.M., " Further Remarks on Sequential Estimation The Exponential Case ", Ann.Math.Statist., 43(4). 1147-1154, (1972) 54. Starr,N.& Uoodroofe,M., "Remarks on Sequential Point Estimation", Proc.Nat.Acad.Sci., U.S.A., 63, 285-188, (1969) 55. Starr N. & Uoodroofe M.,"Remarks on a Stopping Time", Proc.Hat.Acad.Sci., U.S.A., 61, 1215-1218, (1968) 56. Stein C.,"A Two-Sample Test for a Linear Hypothesis whose Power is Independent of the Variance", Ann.Math.Statist., 16, 243-258, (1945) 57. Stein C.,"Some Problems in Sequential Estimation", Econometrica, 17, 77-78, (1949) 58. Wang Y.H.," Sequential Estimation of the Mean Vector of a Multinormal Population ", J.Ame.Statist.Assoc.,75, 977-983,(1988) 59. Wijsman R.A.."Smallest Simultaneous Confidence Sets with Applications in Multivariate Analysis", Multivariate Analysis, V, 483-498, (1980) 60. Woodroofe M.," Second Order Approximations for Sequential Point and Interval Estimation ", Ann.Statist.,5,985-995,(1977) 61. 黃欣伸，”排程的隨機動態規劃模型及其在管理上的應用”國立政治大學統計研究所，(1986) 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/#B2002006233 資料類型 thesis dc.contributor.advisor 余千智 zh_TW dc.contributor.author (作者) 許淑卿 zh_TW dc.creator (作者) 許淑卿 zh_TW dc.date (日期) 1987 en_US dc.date.accessioned 4-五月-2016 17:12:32 (UTC+8) - dc.date.available 4-五月-2016 17:12:32 (UTC+8) - dc.date.issued (上傳時間) 4-五月-2016 17:12:32 (UTC+8) - dc.identifier (其他 識別碼) B2002006233 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/90905 - 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) 論文提要 本論文所擬探討之對象為多變量統計分配函數模擬（Simulation）之最佳停止法則問題（Optimal Stopping Rule Problem），此類問題之目的在於設法利用盡量少的樣本觀察值來求得哭未知母數（Unknown Parameter）的信賴區間（域）（Confidence Interval）（Confidence Region），而此信賴區間（域）之寬度（Width）即包含機率（Coverage Probability）均已事先指定。 以往研究者對於最佳停止法則問題的研究對象多侷限於單變量統計分配函數，而多變量統計分配函數模擬之最佳停止法則問題，仍尚在研究階段，因此本論文之重點乃在於探討如何求得滿足最佳停止法則之最小樣本數。在此我們以多變量常態分配函數為重心，發展出一個以信賴區域體積大小為設限標準的最佳停止法則，同時亦提供了一組實際模擬結果的數值比較與分析。 zh_TW dc.description.tableofcontents 目錄 第一章 緒論………1 第一節 最佳停止法則問題的簡介………1 第二節 研究動機與目的………2 第三節 本文結構………2 第四節 研究方法………3 第五節 研究流程………3 第二章 文獻回顧………4 第三章 單變量分配函數之最佳停止法則………7 第一節 前言………7 第二節 不限母體之單變量分配函數………7 第三節 單變量常態分配函數………9 第四章 多變量分配函數之最佳停止法則………14 第一節 前言………14 第二節 不限母體之多變量分配函數………14 第三節 多變量常態分配函數………15 第五章 以體積為基礎之模擬最佳停止法則──多變量常態分配函數………29 第一節 前言………29 第二節 理論探討與證明………29 第三節 最佳停止法則之產生………33 第六章 數值結果與比較分析………40 第一節 前言………40 第二節 單變量常態分配之電腦模擬………40 第三節 多變量常態分配之電腦模擬………43 第四節 數值結果與比較分析………45 第七章 結論與建議………54 附錄………56 參考書目………79 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002006233 en_US dc.title (題名) 多變量模擬輸出之統計分析 zh_TW dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 參考書目 1. Alan, K & Saxena, K.M. L., " Bounded Length Confidence Interval for a Common Mean ", Commun, Statist.-theor. Meth., 13(17), 2133-2142, (1984) 2. Anderson, T.W., An Introduction to Multivariate Statistical Analysis, 1st ed., Chicherter Brisbane Toronto, Singapore, (1985) 3. Anderson, T.W., "Estimating Linear Restrictions on Regession Co-efficients for Multivariate Normal Distributions", Ann. Math. Statist., 22, 327–351, (1951b) 4. Anscombe, F.J., " Sequential Estimation ", J.R. Statist. Soc. B 15, 1-21, (1953) 5. Atkinson, A.C. & Pearce, M.C., " The Computer Generation of Beta, Gamma and Normal Random Variable ", J. R. Statist.Soc. A 139,431-448, (1976) 6. Basilevsky, A., Applied Matrix Algebra in the Statistical Science, North-Holland, N.Y., (1983) 7. Basu, D., "On Statisticss Independent of a Complete Sufficient Statistic", sankhya, 15, 377-380 8. Chatfield, C. & Collins, A.J., Introduction to Multivariate Analysis, Chapman & Hall, N.Y., (1988) 9. Chew, V., " Confidence, Prediction, and Tolerance Regions for the Multinormal Distribution ", J. Ame. Statist. Assoc. , 605-617, (1966) 10. Chow, Y. S. & Robbins, H., " On the Asymptotic Theory of Fixed-width Sequential Confidence interval for the Mean ", Ann.Math. Statist., 36,457-462, (1965) 11. Constantine, A.G., "Some Non-central Distribution Problems in Multivariate Analysis", Ann. Math. Statist, , 34, 1270-1285, (1963) 12. Constantine, A.G., "The Distribution of Hotelling`s Generalised Too", Ann.Math. Statist. , 37, 215-225, (1966) 13. Farrel, R.H., Techniques of Multivariate Calculation, Springer-Verlag, N.Y., (1976) 14. Fishman, G.S., Principles of Discrete Event Simulation, John Wiley & sons, N.Y., (1981) 15. Ghosh,M. & Mukhopadhyay, N., "Consistency and Asymptotic Efficiency of two-stage and Sequential Procedures", Sankhya, A, 43, 220-227, (1981) 16. Ghosh, M. & Mukhopadhgag, M., "On Two Fundamental Problems of Sequential Estimation", Sankhya, B 38, 203-218, (1976) 17. Ghosh, H. & Mukhopadhyay, N., "Sequential Point Estimation of the Mean when the Distribution is unspecified", Comm. Statist., A, Theory methods, 8, 637-652, (1979) 18. Ghosh, H., Sinha B.K.,& Mukhopadhyay, N., " Multivariate Sequential . Point Estimation ", J.mult analysis, 6, 281-294, (1976) 19. Ghosh, M. & Sen, P.K., " On Two-stage James-stein Estimators ", J. Sequential Analysis, 2, 359-367, (1984) 20. Gleser, L.J., " On the Asymptotic Theory of fixed-size sequential Confidence Bounds for Linear Regression ", Ann.Math. Statist., 36, 463-467, (1965) 21. Hall, P., "Asymptotic Theory of Triple Sampling for Sequential Estimation of a Hean ", Ann. Statist., 9, 1229-1238, (1981) 22. Hayakawa, T., "On the Distribution of a Quadratic form in a Multivariate Normal Sample", Ann. Inst. Statist.Math., 18, 191-210, (1966) 23. John, S., "A Tolerance Region for Hultivariate Normal Distributions", Sankhya, 25, 363-368, (1963) 24. Johnson, R.A. & Wichern, D.W., Applied Multivariate Statistical Analysis, 1st ed., Prentice-Hall, New Jersey, (1982) 25. Khan, R.A., " Sequential Estimation of the Mean Vector of a Multinormal Distribution ", sankhy?, A, 30, 331-334, (1968) 26. Konishi, S., "An Approximation to the Distribution of the Sample Correlation Cofficient", Bometrika, 65, 654-656, (1978a) 27. Krishnaiah, P. KR. & Chang,T.C., "On the Exact Distributions of the Traces of S1 (S1+S2)-1 and S1S2-1", sankhya, s, 34,153-168, (1972) 28. Law, A.M. & Kelton, W.D., Simulation Modeling and Analysis, McGraw-Hill, N.Y. (1982) 29. Lee, Y.S., "Some Results on the Sampling Distribution of the Multivariate Correlation Coefficient", J. Royal Statist.Soc., B, 33, 117-138, (1971b) 30. Loeve, M., Probability Theory I, 4nd ed., Springer-Verlag, N.Y., (1977) 31. Loeve, M., Probability Theory II, 4nd ed., Springer-Verlag, N.Y., (1978) 32. Mallows, C.L., "Latent Vectors of Random Symmetric Matrices", Biometrika, 48, 133-149, (1961) 33. Mood, A.M., "On the Distribution of the Characteristic Roots of Normal Second-Moment Matrices", Ann.Math. Statist., 22, 266-273, (1951) 34. Morgan, B. J.T., Elements of Simulation, 1st ed., Canterbury, U.K., (1986) 35. Muirhead, R.J., Aspects of Multivariate Statistical Theory, John Wiley & Sons, N.Y., (1982) 36. Mukhopadhyay, N., " Fixed-Size Simultaneous Confidence Region for Mean Vector and Dispersion of a Multimormal Dist. ", Calcutta. Statist. Assoc. Bull., 28., 147-152, (1979) 37. Mukhopadhyay, N. & Al-Mousawi, J.S., " Fixed-Size Confidence Region for the Mean vector of a Multinormal Distribution ", Sequential Analysis, 5(2), 139-168, (1986) 38. Nadas, A., " An Extension of a Theorem of Chow and Robbins on Sequential Confidence Intervals for the Mean ", Ann.Math. Statist., 40(2), 667-671, (1967) 39. Nagao, H., "On Some Test Criteria for Covariance Matrix", Ann. Statist., 1, 700-709, (1973a) 40. Pritsker, A.A.B., Introduction to simulation and SLAM II, 2nd ed., John Wiley & Sons, N.Y., (1985) 41. Proschan, F., "Confidence and Tolerance Intervals for the Normal Distribution", J, Ame. Statist. Ass., 48, 550-564, (1953) 42. Ray, W.D., "Sequential Confidence Intervals for the Mean of a Normal Population with Unknown Variance ", J.R. Statist.Soc., B(19), 133-143, (1957) 43. Roy, S.N., Some Aspects of Multivariate Analysis, John Wiley & Sons, N.Y., (1957) 44. Rohatsi, V.K. a. 0` Neill, R.T., " on Sequential Estimation of the Mean Vector of a Multinormal Population ", Ann. Inst. Statist.Math., 25, 321-325, (1973) 45. Seelbinder, B.M., "On Stein’s Two-stage sampling Scheme", Ann.Math. Statist. , 24, 640-649, (1953) 46. Simons, G., "On the Cost of not knowing the variance when Making a fixed width. Confidence Interval for the Mean", Ann.Math. Statist. , 39, 1946-1952, (1968) 47. Siotani, M., "Tolerance Regions for a Multivariate Normal Population", Ann. Inst. Statist.Math., 16, 135-153, (1964) 48. Sinha, B.K. & Mukhopadhyay, N., "Sequential Estimation of a Bivariate Normal Mean Vector ", Sankhya, B, 38, 219-230, (1976) 49. Srivastava, M.S., " on fixed-Width Confidence Bounds for Regression Parameters and Mean Vector ", J.R.Statist.Soc., B(29), 132-140, (1967) 50. Srivastava,M.S.& Khati,C.G., An Introduction to Multivariate Statistical Elsevier North Holland, Inc., (1979) 51. Starr,N., " The Performance of a Sequential Procedure for the Fixed-Width Interval Estimation of the Mean ", Ann.Math.Statist., 37, 36-50, (1966a) 52. Starr,H., " on the Asymptotic Efficiency of a Sequentical Precedure for Estimating the Mean ", Ann.MathiStatist.,37. 1173-1185, (1966b) 53. Starr,N.& Uoodroofe.M., " Further Remarks on Sequential Estimation The Exponential Case ", Ann.Math.Statist., 43(4). 1147-1154, (1972) 54. Starr,N.& Uoodroofe,M., "Remarks on Sequential Point Estimation", Proc.Nat.Acad.Sci., U.S.A., 63, 285-188, (1969) 55. Starr N. & Uoodroofe M.,"Remarks on a Stopping Time", Proc.Hat.Acad.Sci., U.S.A., 61, 1215-1218, (1968) 56. Stein C.,"A Two-Sample Test for a Linear Hypothesis whose Power is Independent of the Variance", Ann.Math.Statist., 16, 243-258, (1945) 57. Stein C.,"Some Problems in Sequential Estimation", Econometrica, 17, 77-78, (1949) 58. Wang Y.H.," Sequential Estimation of the Mean Vector of a Multinormal Population ", J.Ame.Statist.Assoc.,75, 977-983,(1988) 59. Wijsman R.A.."Smallest Simultaneous Confidence Sets with Applications in Multivariate Analysis", Multivariate Analysis, V, 483-498, (1980) 60. Woodroofe M.," Second Order Approximations for Sequential Point and Interval Estimation ", Ann.Statist.,5,985-995,(1977) 61. 黃欣伸，”排程的隨機動態規劃模型及其在管理上的應用”國立政治大學統計研究所，(1986) zh_TW
