伯氏多項式對部份單峰迴歸之最大概似估計

迴歸曲線的估計是統計上的一個重要的問題, 而部份線性模型方面有很多的應用. 如Hardle 等人(2000) 所舉的例子: Engle, Granger, Rice 和 Weiss(1986) 是最早考慮部份線性模型, 他們分析了溫度和電力使用的關係. 若迴歸曲線為單峰, 在Cheng (2010) 的碩士論文中, 用伯氏多項式來描述其形狀, 並且用貝氏的方法估計, 而本篇論文在同樣的架構下, 用不同的統計方法-最大概似估計, 來估計其參數, 這是本篇論文主要貢獻. 並且做比較. 演算法是用馬可夫鏈蒙地卡羅方法來尋找M.L.E., 程式為R.

關鍵字

馬可夫鏈蒙地卡羅；最大概似估計；單峰迴歸；伯氏多項式

並列摘要

”The estimator of regression curve” is an important issue in the field of statistics, and there are many applications in ”partial linear model”, like examples given by Hardle (2000). Engle, Granger, Rice and Weiss(1986) are the people who first took ”partial linear model” into considerarion. They analyzed the relationship between temparature and the use of electricity. In the master thesis/dissertaion of Cheng (2010), if regression curve is unimodal, we can use Bernstein Polynomial to describe its shape and estimate it by Bayesian method. The main contribution of this thesis is to use a different statistic method-”Maximun Likelihood Estimator” to estimate ”parameter value” under the same construction, as well as making a comparison. The method of calculation is to apply ”M.C.M.C.” in search of M.L.E., using the program ”R.”

並列關鍵字

Markov Chain Monte Carlo ； Bernstein Polynomial ； Unimodal Regression ； Maximum Likelihood Estimator

參考文獻

[1] 王國龍, (2010). Least Square Method for Concave Regression. Department of

Mathematics, Tamkang University, Master Thesis.

[2] Chang, I. S., Chien, L. C., Hsiung, C. A., Wen, C. C. and Wu, Y. J. (2006). Shape restricted regression with random Bernstein polynomials. Accepted for the Vardi Volume, IMS Lecture Notes - Monograph Series.

[3] Chang, I. S., Hsiung, C. A., Wu, Y. J. and Yang, C. C. (2005). Bayesian survival analysis using Bernstein polynomials. Scandinavian Journal of Statistics 32, 447-466.

[4] Cheng, L. H. (2010). Partial Unimodal Bayesian Regression Using Bernstein Polynomial. Department of Applied Mathematics, Chung Yuan Christian University, master thesis.

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伯氏多項式對部份單峰迴歸之最大概似估計

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