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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張淑惠 | |
| dc.contributor.author | Yu-Che Tseng | en |
| dc.contributor.author | 曾郁哲 | zh_TW |
| dc.date.accessioned | 2021-06-08T06:03:05Z | - |
| dc.date.copyright | 2011-10-03 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-08-05 | |
| dc.identifier.citation | Battista, T. D. (2003). Resampling methods for estimating dispersion indices in random and adaptive designs. Environmental and Ecological Statistics, 10, 83-93
Bera, A. K., and Bilias, Y. (2001). Rao’s score, Neyman’s C(α) and Silvey’s LM tests : an essay on historical developments and some new results. Journal of Statistical Planning and Inference, 97, 9-44 Broek, J. V. D. (1995). A score test for inflation in a Poisson distribution. Biometrics, 51, 738-743 Cameron, A. C., and Triedi, P. K.(1986). Econometric models based on count data comparisons and applications of some estimators and tests. Journal of Applied Econometrics, 1, 29-53 Cameron, A. C., and Trivedi, P. K.(1998). Regression Analysis of Count Data. Cambridge. Casella, G., and Berger, R. L. (2002). Statistical Inference. Thomson Learning. Conway, R. W., and Maxwell, W. L. (1962). A queuing model with state dependent service rates. J. Am. Statist. Ass, 87, 451-457 Consul, P. G., and Jain, G. C. (1973). A generalization of the Poisson distribution. Technometrics, 15, 791-799 Cox, D. R. (1983). Some remarks on overdispersion. Biometrika, 70, 269-274 Dean, C. B. (1992). Testing for overdispersion in Poisson and Binomial regression models. JASA, 87, 451-457 Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. JRSSB, 39, 1-38 Deng, D., and Paul, S. R. (2005) Score tests for zero-infaltion and over-dispersion in generalized liner models. Statistica Sinica, 15, 257-276 Dobson, A. J., and Barnett, A. G. (2002). Introduction to Generalized Linear Models . Boca Raton, FL: Chapman and Hall/CRC. Engle, R. F. (1984). Wald , likelihood ration , and Langrange multiplier tests in econometrics. Handbook of Econometrics. Guikema, S. D., and Goffelt, J. P. (2008). A flexible count data regression model for risk analysis. Risk Analysis, 28 Gupta, P. L., Gupta, R. C., and Tripathi, R. C. (2005). Score test for zero inflated generalized Poisson regression model. Commun. Stat. Theory meth, 33, 47-64 Hardin, J. W., and Hilbe, J. M. (2007). Generalized Linear Models and Extensions. College Statistic: Stata Press. Johnson, N. L., Kotz, S., and Kemp, A.W. (1992). Univariate Distributions. New York, John Wiley. Kokonendji, C. C., Mizere, D., and Balakrishnan, N. (2008). Connections of the Poisson weight function to overdispersion and underdispersion. J. Statist. Plann. Inference, 138, 1287-1296 Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, 34, 1-14 Lord, D., Srinivas, R. G., and Seth, D. G. (2010). Extension of the aplication of Conway-Maxwell-Poisson models: analyzing traffic crash data exhibiting underdispersion. Risk Analysis, 30 McCullagh, P., and Nelder, J. A. (1989). Generalized Linear Models. Chapman and Hall. Melkersson, M., and Rooth D.O. (2000). Modeling female fertility using inflated count data models. J Popul Econ, 13, 189-203 Rao, C. R. (2002). Linear Statistics Inference and its Application. JOHN WIELY & SONS , INC. Rao, C. R. (1947). Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Mathematical Proceedings of the Cambridge Philosophical Society, 44, 50-57 Ridout, M., Hinde, J., and Demetrio, C. G. B. (2001). A score test for testing a zero-inflated Poisson regression model against zero-infalted negative binomial alternatives. Biometrics, 57, 219-223 Sellers, K. F., and Shmueli, G. (2010). A flexible regression model for count data. The Annals of Applied Statistics, 4, 943-961 Shmueli, G., Minka, T. P., Kadane, J. B., Borle, S., and Boatwright, P. (2005). A useful distribution for fitting discrete data : revival of the Conway-Maxwell-Poisson distribution. Appl Statist, 54, 127-142 Simonoff, J. S. (2003). Analyzing Categorical Data.Springer. Wedderburn, R. W. M. (1974). Quasi-likelihood function, generalized linear models, and the Gauss-Newton method. Biometrika, 61, 439-447 Winkelman, R., and Zimmermann, K. F. (1991). A new approach for modeling economic count data. Economics Letters, 37, 139-143 Winkelmann, R. (2008). Econometric Analysis of Count Data. Springer. Yang, Z., Hardin, J. W., Addy, C. L., and Voung, Q. H. (2007). Testing approaches for overdispersion in Poisson regression versus the generalized Poisson model. Biometrical Journal, 49, 565-584 Yang, Z., Hardin, J. W., and Addy, C. L. (2009). Testing overdispersion in the zero-inflated Poisson model. Journal of Statistical Planning and Inference, 139, 3340-3353 Yang, Z., Hardin, J. W., and Addy, C. L. (2010). Score tests for overdispersion in zero-inflated Poisson mixed models. C.S.D.A., 54, 1234-1246 Xiang, L., Lee, A. H., Yau, K. K. W., and McLachlan, G. J. (2007). A Score test for overdispersion in zero-inflated Poisson mixed model. Statist. Med., 26, 1608-1622 Xie, F. C., Wei, B. C., and Lin, J. G. (2009). Score tests for zero-inflated generalized Poisson mixed models. C.S.D.A., 53, 3478-3489 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/25130 | - |
| dc.description.abstract | 計次資料配適卜瓦松回歸模型中，一個常見的問題為過度分散現象，而零膨脹為造成此現象的原因之一。Cox(1983)是第一個提出方法來檢定過度分散存在與否；Dean(1992)稍後提出了另一種方法。而Dean(1992)提出的方法比Cox(1983) 略勝一籌的原因是:Cox(1983)的檢測過程中沒有共變數，而Dean則有。此外，除了過度分散的問題之外，另一個統計問題則是不足分散現象。當在資料中發現變異數大於期望值，稱之為過度分散；反之，則為不足分散。由此兩種現象被統稱為非均等分散。雖然已經有許多檢定方法提出檢定過度分散現象，但僅以有限分數檢定檢定量方法檢定不足分散現象，且少考有考慮零膨脹現象之外所造成之過度分散與不足分散情況。因此本論文，使用COM-卜瓦松分布來求得非均等分散檢定統計量，並延伸其方法到其它膨脹狀況，最後以模擬來驗證此方法。 | zh_TW |
| dc.description.abstract | A common problem in fitting count data with Poisson regression model is overdispersion, zero-inflation is one of the causes. Cox(1983) is the first one who proposed tests for the existence of overdispersion. Dean(1992) proposed another method. The reason that what Dean(1992) proposed is better than Cox(1983) is that Cox(1983) method proceeds tests without covariates, but Dean’s method did. In addition to the overdispersion problem, another statistical issue is underdispersion. When data show that variance is greater than mean, it is called overdispersion. In contrast, call underdispersion. Both types of data are called unequi-dispersed. Although many methods had been proposed to test overdispersion, limited methods have dealt with test for underdispersion using score test statistic and take into the account situations beyond zero-inflated over- or underdispersion. In this thesis, we use COM-Poisson distribution to derive unequi-dispersion test statistic, and extend the methods to other inflated cases, and conduct simulations to justify our methods. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T06:03:05Z (GMT). No. of bitstreams: 1 ntu-100-R98842013-1.pdf: 1796529 bytes, checksum: ad54cfef0fd91d7db34998d44d7de8ce (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | 第一章 緒論 1
第一節 研究背景 1 第二節 研究目的 3 第三節 論文架構 4 第二章 文獻探討 5 第一節 分數檢定統計量 5 第二節 零膨脹模型 7 第三節 分散分布及其相關分散檢定統計量 8 第四節 COM-卜瓦松分布 14 第三章 研究方法 16 第一節 廣泛膨脹卜瓦松回歸模型及其分數檢定統計量 16 第二節 廣泛膨脹卜瓦松回歸模型之分散分數檢定統計量 20 第四章 模擬 25 第一節 模擬資料之產生 25 第二節 模擬結果 27 第五章 結果與討論 38 參考文獻 40 附錄一 44 附錄二 47 附錄三 49 表目錄 表一 資料型態 8 表二 Dean(1992)不同變異數型式下之過度分散現象分數檢定統計量 11 表三 無共變數廣泛膨脹分數檢定統計量之經驗檢定力 27 表四 有共變數廣泛膨脹分數檢定統計量之經驗檢定力 27 表五 負二項資料無共變數過度分散之經驗檢定力 31 表六 廣義卜瓦松資料無共變數過度分散之經驗檢定力 31 表七 廣義卜瓦松資料無共變數不足分散之經驗檢定力 32 表八 COM-卜瓦松資料無共變數過度分散之經驗檢定力 32 表九 COM-卜瓦松資料無共變數不足分散之經驗檢定力 33 表十 COM-卜瓦松資料有共變數過度分散之經驗檢定力 36 表十一 COM-卜瓦松資料有共變數不足分散之經驗檢定力 36 表十二 膨脹現象與分布假設錯誤之分散現象 39 圖目錄 圖一 廣泛膨脹卜瓦松不同情況下之變異數除以期望值 17 圖二 近似值跟真實值的相差圖 23 圖三 無共變數檢定廣泛膨脹之經驗檢定力圖 28 圖四 無共變數廣泛膨脹分數檢定統計量之Q-Q plots跟經驗分布 28 圖五 有共變數檢定廣泛膨脹之經驗檢定力圖 29 圖六 有共變數廣泛膨脹分數檢定統計量之Q-Q plots跟經驗分布 29 圖五 負二項資料之比較經驗檢定力圖 33 圖六 廣義卜瓦松資料之比較經驗檢定力圖 34 圖七 COM-卜瓦松資料之之比較經驗檢定力圖 34 圖八 無共變數COM-卜瓦松分散性分數檢定統計量之Q-Q plots 35 圖九 無共變數COM-卜瓦松分散性分數檢定統計量之經驗分布 35 圖十 有共變數COM-卜瓦松分散性分數檢定統計量之Q-Q plots 37 圖十一 有共變數COM-卜瓦松分散性分數檢定統計量之經驗分布 37 | |
| dc.language.iso | zh-TW | |
| dc.subject | COM-卜瓦松分布 | zh_TW |
| dc.subject | 不足分散現象 | zh_TW |
| dc.subject | 分數檢定 | zh_TW |
| dc.subject | 過度分散現象 | zh_TW |
| dc.subject | 廣泛膨脹現象 | zh_TW |
| dc.subject | COM-Poisson distribution | en |
| dc.subject | Underdispersion | en |
| dc.subject | Score test | en |
| dc.subject | Overdispersion | en |
| dc.subject | Generalization inflated | en |
| dc.title | 廣泛膨脹卜瓦松回歸模型之分散性分數檢定統計量 | zh_TW |
| dc.title | Score Test for Dispersion in Generalized Inflation of Poisson Regression Model | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 戴政 | |
| dc.contributor.oralexamcommittee | 陳秀熙,黃昆明,鄭明燕 | |
| dc.subject.keyword | COM-卜瓦松分布,不足分散現象,分數檢定,過度分散現象,廣泛膨脹現象, | zh_TW |
| dc.subject.keyword | COM-Poisson distribution,Generalization inflated,Overdispersion,Score test,Underdispersion, | en |
| dc.relation.page | 53 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2011-08-05 | |
| dc.contributor.author-college | 公共衛生學院 | zh_TW |
| dc.contributor.author-dept | 流行病學與預防醫學研究所 | zh_TW |
| 顯示於系所單位： | 流行病學與預防醫學研究所 | |
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