隨機伯氏多項式模型的凹向下迴歸分析之最大概似估計

Maximum Likelihood Estimator in Concave Regression Analysis with Random Bernstein Polynomial Model

鍾淑婷(Su-Ting Chung)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/碩士(2010年)

https://doi.org/10.6840/cycu201000172

摘要

估計迴歸曲線在統計上是重要的, 所以本篇論文主要提供對
凹口向下迴歸曲線估計的一個方法。利用到半導體工業上, 產
品的預燒時間(Burn-in time) 和使用期限之間的關係, 當預
燒時間太少或太多, 都會造成產品本身的不耐用或損壞。因
此預燒時間對保存期限就會形成凹口向下單峰之關係.
(見Boukai, 1987)。
本篇論文是用伯氏多項式去描述迴歸曲線為凹向下的各種
形狀作並做有系統的整理和研究, 詳細可參見(Chang 等人
2007), 其中包括凹口向下且遞增和單峰凹口向下, 但我們使
用最大概似估計法並且用馬可夫蒙地卡羅(M. C. M. C.) 之
方法去找尋M.L.E.參數, 其模擬計算相當的不錯, 呈現在論
文的最後部份。

關鍵字

馬可夫鏈蒙地卡羅 ； 伯氏多項式 ； 凹口向下

並列摘要

We want to investigate the relationship between independent variable and dependent variable, especially to make a study of regression curve in statistics. So this paper mainly provides
method of regression curve. If the regression curve is unimodal concave down, it looks like relations between Burn-in time and life of products in industry. When the Burn-in time are too short or too long, it could make the industrial products unstable. Therefore the Burn-in time in relation to life of products
performs a constraint shape (Boukai, 1987). This paper aims at the regression curve to make for concave each kind of graph have the system of the reorganization and the research, seen in
(Chang 2007),that includes concave-increasing and unimodalconcave down, makes the estimate with MLE, and also writes down their integrity to develop the algorithm. named independent Metropolis Algorithm . The MCMC method is to applied estimate calculates that is pretty good and presents in final part of the paper.

並列關鍵字

Markov chain Monte Carlo ； Bernstein Polynomial ； concave down

參考文獻

Y. J. (2007). Shape restricted regression with random Bernstein

Notes-Monograph Series, Vol. 54, 187-202

Green, P. G. (1995). Reversible jump Markov chain Monte Carlo

computation and Bayesian model determination. Biometrika 82,

Robert, C. P. & Casella, G. (1999). Monte Carlo statistical methods.