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題名 貝氏方法應用於隨機化作答模式之研究
A Bayesian Approach to Randomized Response Model作者 黃馨慧 貢獻者 鄭天澤
黃馨慧關鍵詞 隨機化作答模式
敏感性問題
貝氏方法
事前資訊日期 2009 上傳時間 1-Jul-2013 17:00:43 (UTC+8) 摘要 當作敏感性的議題調查時，如：性行為、未婚懷孕、墮胎…等若使用直接詢問(direct response)的方式，受訪者可能為顧及其隱私而拒絕回答或是不誠實作答，故在進行統計推論時恐有偏誤產生。為解決上述問題，Warner(1965)首先提出隨機化作答模式(randomized response model)，而後有許多學者，如Greenberg等人(1969)、Mangot & Singh(1990)…等提出新的隨機化作答模式，以修正Warner的模式改善估計效率。然而Winkler & Franklin(1979)首先指出，「在隨機化的過程中會減少樣本所提供的資訊」，而結合事前資訊(prior information)貝氏估計法(Bayesian method)能彌補此缺點。其次，Pitz(1980)使用貝氏估計解決Fidler & Kleinknecht(1977)中的不合理估計值。第三，之後其他學者亦驗證在某些情況下，貝氏估計量的效率高於MLE。基於上述三個原因，本研究使用貝氏方法估計Huang(2004)隨機化作答模式的參數，結果證明能產生合理之貝氏估計值，且在某些情況下，其貝氏估計量的效率高於MLE。 參考文獻 Abul-Ela, A. L. A., Greenberg, B. G., and Horvitz, D. G. (1967). “A Multi-Proportional Randomized Response Model,” Journal of the American Statistical Association, 62, 990-1008.Bar-Lev, S. K., Bobovich, E., and Boukai, B. (2003). “A Common Conjugate Prior Structure for Several Randomized Response Models,” TEST, 12, 101-113.Barabesi, L., & Marcheselli, M. (2006). “A Generalization of Huang’s Randomized Response Procedure for the Estimation of Population Proportion and Sensitivity Level.” Metron, vol. LXIV, n. 2, pp. 145-159.Chang, H. J., and Huang, K. C. (2001). “Estimation of Proportion and Sensitivity of a Qualitative Character,” Metrika, 53, 269-280.Chang, H. J., and Liang, D. H. (1996a). “A Two-Stage Unrelated Randomized Response Procedure for,” Australian journal of statistics, 38, 43-51.Chang, H. J., and Liang, D. H. (1996b). “A Randomized Response Procedure for Two-Unrelated Sensitive Questions,” Journal of Information & Optimization Sciences, 17, 185-198.Chaubey, Y.,and Li, W. (1995). “Comparison between Maximum Likelihood and Bayes Methods for Estimation of Binominal Probability with Sample Compositing,” Journal of Official Statistics, 11,379-390.Chaudhuri, A., Mukerjee, R. (1988). Randomized Response: Theory and Techniques. Marcel Dekker, New York. Christofides, T. C. (2003). “A Generalized Randomized Response Technique,” Metrika, 57, 195-200.Christofides, T. C. (2005). “Randomized Response in Stratified Sampling,” Journal of Statistical Planning and Inference, 128, 303-310.Fidler, D. S., and Kleinknecht, R. E. (1977). “Randomized Response Versus Direct Questioning: Two Data-Collection Methods for Sensitive Information,” Psychological Bulletin, 84, 1045-1049.Greenberg, B. G., Abul-Ela, A. L. A., Simmons, W. R., and Horvitz, D. G. (1969). “The Unrelated Question Randomized Response Model: Theoretical Framework,” Journal of American Statistical Association, 64, 520-539.Greenberg, B. G., Kuebler, R. R., Jr., Abernathy, J. R., and Horvitz, D. G. (1971). “Application of the Randomized Response Technique in Obtaining Quantitative Data,” Journal of American Statistical Association, 66, 243-250.Huang, K. C. (2004). “A Survey Technique for Estimating the Proportion and Sensitivity in a Dichotomous Finite Population,” Statistica Neerlandica, 58, 75-82.Kim, J. M., Tebbs J. M., and An S. W. (2006). “Extensions of Mangat’s Randomized Response Model,” Journal of Statistical Planning and Inference, 136, 1554-1567.Kim, J. M., and Warde, W. D. (2004). “A Stratified Warner’s Randomized Response Model,” Journal of Statistical Planning and Inference, 120, 155-165.Kuk, A. Y. C. (1990). “Asking Sensitive Questions Indirectly,” Biometrika, 77, 436-438.Mangat, N. S., and Singh, R. (1990). “An Alternative Randomized Response Procedure,” Biometrika, 77, 439-442.Mangat, N. S. (1994). “An Improved Randomized Response Strategy,” Journal of the Royal Statistical Society: Series B, 1, 93-95.Migon, H. S., and Tachibana, V. M. (1997). “Bayesian Approximations in Randomized Response Model,” Computational Statistics & Data Analysis, 24, 401-409.Pitz, G. F. (1980). “Bayesian Analysis of Random Response Models,” Psychological Bulletin, 87, 209-212.Singh, J. (1976). “Randomized Response a Method for Sensitive Surveys.” In Proceedings of the Social Statistics Section, p. 722. American Statistical Association.Winkler, R. L., and Franklin, L. A. (1979). “Warner’s Randomized Response Model: A Bayesian Approach,” Journal of the American Statistical Association, 74, 207-214.Warner, S. L. (1965). “Randomized Response : A Survey Technique for Estimating Evasive Answer Bias,” Journal of the American Statistical Association, 60, 63-69.王智立、蔡宛容，2007。應用一般化Greenberg無關聯隨機化作答模式於敏感問題之研究，中國統計學報，第45卷，頁189-205。 描述 碩士
國立政治大學
統計研究所
96354003
98資料來源 http://thesis.lib.nccu.edu.tw/record/#G0096354003 資料類型 thesis dc.contributor.advisor 鄭天澤 zh_TW dc.contributor.author (Authors) 黃馨慧 zh_TW dc.creator (作者) 黃馨慧 zh_TW dc.date (日期) 2009 en_US dc.date.accessioned 1-Jul-2013 17:00:43 (UTC+8) - dc.date.available 1-Jul-2013 17:00:43 (UTC+8) - dc.date.issued (上傳時間) 1-Jul-2013 17:00:43 (UTC+8) - dc.identifier (Other Identifiers) G0096354003 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58662 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計研究所 zh_TW dc.description (描述) 96354003 zh_TW dc.description (描述) 98 zh_TW dc.description.abstract (摘要) 當作敏感性的議題調查時，如：性行為、未婚懷孕、墮胎…等若使用直接詢問(direct response)的方式，受訪者可能為顧及其隱私而拒絕回答或是不誠實作答，故在進行統計推論時恐有偏誤產生。為解決上述問題，Warner(1965)首先提出隨機化作答模式(randomized response model)，而後有許多學者，如Greenberg等人(1969)、Mangot & Singh(1990)…等提出新的隨機化作答模式，以修正Warner的模式改善估計效率。然而Winkler & Franklin(1979)首先指出，「在隨機化的過程中會減少樣本所提供的資訊」，而結合事前資訊(prior information)貝氏估計法(Bayesian method)能彌補此缺點。其次，Pitz(1980)使用貝氏估計解決Fidler & Kleinknecht(1977)中的不合理估計值。第三，之後其他學者亦驗證在某些情況下，貝氏估計量的效率高於MLE。基於上述三個原因，本研究使用貝氏方法估計Huang(2004)隨機化作答模式的參數，結果證明能產生合理之貝氏估計值，且在某些情況下，其貝氏估計量的效率高於MLE。 zh_TW dc.description.tableofcontents 第一章、 緒論 8第一節、 研究動機與背景 8第二節、 研究目的 9第三節、 研究架構 9第二章、 文獻探討 10第一節、 直接詢問法 10第二節、 Warner的隨機化作答模式 11第三節、 Huang的隨機化作答模式 14第四節、 貝氏方法 15第五節、 貝氏方法估計隨機化作答模式之參數 16一、 Winkler & Franklin(1979)的研究 16二、 Pitz(1980)的研究 19第三章、 貝氏分析 21第一節、 貝氏估計量的推導 21第二節、 評估估計量的方法 24第四章、 數值運算 28第一節、 參數設定說明 28第二節、 數值模擬結果 29第五章、 結論與建議 61第一節、 結論 61第二節、 建議 61參考文獻 63 zh_TW dc.format.extent 1078482 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0096354003 en_US dc.subject (關鍵詞) 隨機化作答模式 zh_TW dc.subject (關鍵詞) 敏感性問題 zh_TW dc.subject (關鍵詞) 貝氏方法 zh_TW dc.subject (關鍵詞) 事前資訊 zh_TW dc.title (題名) 貝氏方法應用於隨機化作答模式之研究 zh_TW dc.title (題名) A Bayesian Approach to Randomized Response Model en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) Abul-Ela, A. L. A., Greenberg, B. G., and Horvitz, D. G. (1967). “A Multi-Proportional Randomized Response Model,” Journal of the American Statistical Association, 62, 990-1008.Bar-Lev, S. K., Bobovich, E., and Boukai, B. (2003). “A Common Conjugate Prior Structure for Several Randomized Response Models,” TEST, 12, 101-113.Barabesi, L., & Marcheselli, M. (2006). “A Generalization of Huang’s Randomized Response Procedure for the Estimation of Population Proportion and Sensitivity Level.” Metron, vol. LXIV, n. 2, pp. 145-159.Chang, H. J., and Huang, K. C. (2001). “Estimation of Proportion and Sensitivity of a Qualitative Character,” Metrika, 53, 269-280.Chang, H. J., and Liang, D. H. (1996a). “A Two-Stage Unrelated Randomized Response Procedure for,” Australian journal of statistics, 38, 43-51.Chang, H. J., and Liang, D. H. (1996b). “A Randomized Response Procedure for Two-Unrelated Sensitive Questions,” Journal of Information & Optimization Sciences, 17, 185-198.Chaubey, Y.,and Li, W. (1995). “Comparison between Maximum Likelihood and Bayes Methods for Estimation of Binominal Probability with Sample Compositing,” Journal of Official Statistics, 11,379-390.Chaudhuri, A., Mukerjee, R. (1988). Randomized Response: Theory and Techniques. Marcel Dekker, New York. Christofides, T. C. (2003). “A Generalized Randomized Response Technique,” Metrika, 57, 195-200.Christofides, T. C. (2005). “Randomized Response in Stratified Sampling,” Journal of Statistical Planning and Inference, 128, 303-310.Fidler, D. S., and Kleinknecht, R. E. (1977). “Randomized Response Versus Direct Questioning: Two Data-Collection Methods for Sensitive Information,” Psychological Bulletin, 84, 1045-1049.Greenberg, B. G., Abul-Ela, A. L. A., Simmons, W. R., and Horvitz, D. G. (1969). “The Unrelated Question Randomized Response Model: Theoretical Framework,” Journal of American Statistical Association, 64, 520-539.Greenberg, B. G., Kuebler, R. R., Jr., Abernathy, J. R., and Horvitz, D. G. (1971). “Application of the Randomized Response Technique in Obtaining Quantitative Data,” Journal of American Statistical Association, 66, 243-250.Huang, K. C. (2004). “A Survey Technique for Estimating the Proportion and Sensitivity in a Dichotomous Finite Population,” Statistica Neerlandica, 58, 75-82.Kim, J. M., Tebbs J. M., and An S. W. (2006). “Extensions of Mangat’s Randomized Response Model,” Journal of Statistical Planning and Inference, 136, 1554-1567.Kim, J. M., and Warde, W. D. (2004). “A Stratified Warner’s Randomized Response Model,” Journal of Statistical Planning and Inference, 120, 155-165.Kuk, A. Y. C. (1990). “Asking Sensitive Questions Indirectly,” Biometrika, 77, 436-438.Mangat, N. S., and Singh, R. (1990). “An Alternative Randomized Response Procedure,” Biometrika, 77, 439-442.Mangat, N. S. (1994). “An Improved Randomized Response Strategy,” Journal of the Royal Statistical Society: Series B, 1, 93-95.Migon, H. S., and Tachibana, V. M. (1997). “Bayesian Approximations in Randomized Response Model,” Computational Statistics & Data Analysis, 24, 401-409.Pitz, G. F. (1980). “Bayesian Analysis of Random Response Models,” Psychological Bulletin, 87, 209-212.Singh, J. (1976). “Randomized Response a Method for Sensitive Surveys.” In Proceedings of the Social Statistics Section, p. 722. American Statistical Association.Winkler, R. L., and Franklin, L. A. (1979). “Warner’s Randomized Response Model: A Bayesian Approach,” Journal of the American Statistical Association, 74, 207-214.Warner, S. L. (1965). “Randomized Response : A Survey Technique for Estimating Evasive Answer Bias,” Journal of the American Statistical Association, 60, 63-69.王智立、蔡宛容，2007。應用一般化Greenberg無關聯隨機化作答模式於敏感問題之研究，中國統計學報，第45卷，頁189-205。 zh_TW
