一個新的適合度檢定法

魏名君(MING-CHUN WEI)

指導教授 ： 鄒宗山

國立中央大學/理學院/統計研究所/碩士(2014年)

摘要

統計分析的正確性取決於使用正確或合理的分配函數來配適資料，而適合度檢定是用來驗證使用的模型是否合適的方法。基於廣義線性模型的參數估計量是否有一致性，本論文提出一個新的統計量來進行適合度檢定，其中探討的重點在於資料是否來自伽瑪、韋伯或對數常態迴歸模型。我們使用模擬研究與實例分析來比較我們的方法與Kolmogorov-Smirnov Kolmogorov, 1933; Smirnov, 1939 、Cramér-von Mises Cramér, 1928; von Mises, 1931 與Anderson-Darling 1952 等三個使用經驗分配函數的適合度檢定統計量。

關鍵字

適合度檢定 ； 伽瑪迴歸模型 ； 韋伯迴歸模型 ； 對數常態迴歸

並列摘要

We propose new goodness fit of test approaches that are easy to implement with the bootstrapping techniques. The techniques are instituted by taking advantage of the fact that the mean regression parameters can be consistently estimated by using normal, gamma and Poisson models even when model fails. We test the appropriateness of the Weibull, log-normal and gamma model assumptions to illustrate the merit of our new methods.
We also compare our novel approaches with several commonly used and implemented existing methods with simulations and real data analyses.

並列關鍵字

goodness of fit ； gamma regression model ； Weibull regression model ； log-normal regression model

參考文獻

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3. Brynjarsdóttir, J. and Stefánsson, G. (2004). Analysis of cod catch data from Icelandic groundfish suveys using generalized linear model. Fisheries Research, 70, 195-208.

4. Cramér, H. (1928). On the composition of elementary errors, Scandinavian Actuarial Journal, 11, 13-74 and 141-180.

6. Gupta, R. D., Kundu, D. and Manglick, A. (2002). Probability of correct selection of gamma versus GE or Weibull versus GE models based on likelihood ratio test. Recent Advances in Statistical Methods (Editor: Chaubey, Y. P.), Publisher World Scientific Publishing Company Inc., London, 147-156.