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研究生:洪雅鈴
研究生(外文):Ya-Ling Hung
論文名稱:連結函數之有母數強韌推論
論文名稱(外文):The robust reference of parametric
指導教授:鄒宗山鄒宗山引用關係
學位類別:碩士
校院名稱:國立中央大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:89
中文關鍵詞:連結函數
外文關鍵詞:link function
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  • 被引用被引用:0
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  • 下載下載:11
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摘要
Tsou (2004)將Royall and Tsou (2003)提出之強韌概似函數的方法推廣到在廣義線性模型之下迴歸係數推論上,進而提出了概似函數的修正法。而修正過的概似函數,在大樣本時,只要觀察值的真正分配有二階動差,便可對迴歸係數提供正確的推論。Tsou (2003)則是利用同樣強韌概似函數的方法提出了具有強韌性的有母數檢定法來比較分配未知的母體變異數。
本研究將把上述的強韌法推廣到連結函數的強韌推論上。將常態、伽瑪和逆高斯實作模型進行修正,得到在大樣本時及一些正規條件下正確的連結函數的概似函數。並利用修正後的強韌概似比檢定、分數檢定以及Wald檢定來顯示此強韌性。另外,也對常被用分析個數資料的卜瓦松迴歸模型進行修正。
Abstract
Tsou (2004) extends the robust likelihood functions that was proposed by Royall and Tsou (2003) to the reference of the regressive coefficients in general linear model, and proposes the adjust method of likelihood functions. In large sample, if true distribution of observations just has the second moment, the likelihood functions that have been adjusted will provide the correct reference for regressive coefficients. Tsou (2003) applied the similar method that proposed the testing method of robust parametric to compare the population variance of unknown distribution.
In this paper, we apply the robust method of the above to the robust reference of link functions. According to the adjusted working model of normal, gamma and inverse gauss, we get the likelihood functions of the correct link functions in large sample and in some regular conditions. We show that it is robust by the adjusted robust likelihood test, score test and Wald test. Furthermore, we adjust the Poisson working model that are often used to analyse the count data.
〜目錄〜
第1章 緒論 ………………………………………………………1
第2章 回顧相關文獻 ……………………………………………3
2.1 回顧相關文獻 ………………………………………………3
2.2 強韌概似函數 ………………………………………………4
第3章 修正項 ………………………………………………………8
3.1 常態實作模型的修正項 ……………………………………8
3.2 伽瑪實作模型的修正項……………………………………23
3.3 逆高似實作模型的修正項…………………………………38
3.4 卜瓦松實作模型的修正項…………………………………53
第4章 模擬研究……………………………………………………67
4.1 強韌常態迴歸………………………………………………68
4.2 強韌伽瑪迴歸………………………………………………69
4.3 強韌逆高斯伽瑪迴歸………………………………………71
4.4 強韌卜瓦松迴歸……………………………………………73
第5章 結論…………………………………………………………87
參考文獻 ………………………………………………………………88
參考文獻
Cheng, K. F., and Wu, J. W. (1994).Testing goodness of fit for a parametric
of link functions. JASA, 89, 657-664.

Joglekar, G., Schuenemeyer, J. H. and LaRiccia, V. (1989). Lack-of-fit testing when replicates are not available. Amer. Stat., 43, 135-143.

McCullagh, P. and Nelder, J. A. (1989). Generalized linear models. 2nd
Ed. New York: Chapman and Hall.

Pregibon, D. (1980). Goodness of link tests for generalized linear models.
Applied Statistics, 29, 15-23.

Raymond, H. M., Douglas, C. M., and Vining, G. G. (2002). Generalized linear models with applications in engineering and the sciences. New York : John Wiley.

Royall, R. M., and Tsou, T. S. (2003). Interpreting statistical evidence using imperfect models: robust adjusted likelihood functions. J. R. Statist. Soc. B. 65, 391-404.

Su, J. Q., and Wei, L. J. (1991). A lack of fit test for the mean function in a generalized linear model. JASA, 86, 420-426.

Tsiatis, A. A. (1980). A note on a goodness of fit test for the logistic regression model. Biometrics, 32, 761-768.

Tsou (2003). Comparing two population means and variances–A parametric robust way. Comm. in. Stat-Theo and Meth., 32, 2013-2019.

Tsou (2004). Parametric robust inferences for regression parameters under generalized linear models. (submitted.)

White, H. (1982). Maximum likelihood estimation of misspecified models.
Econometrica, 50, 1-25.

Wu, J. W., and Lee, W. C. (2001). The quasi-score statistic in quasi-likelihood model. Statistics, 35, 523-535.
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