臺灣博碩士論文加值系統

在本論文中，於簡單線性迴歸模型下殘差具有MA過程的均勻實驗設計中，我們提出一個選擇最佳的實驗順序之方法。更明確的說即在研究有關均勻設計中殘差是MA(1)過程或是某個特例的MA(k)過程下的最佳實驗順序，其中k是任意的正整數。由於一般要對殘差項的相關性矩陣給一個好的估計通常是不容易的，因此使用改變變異函數(CVF)來瞭解殘差項是無相關性或連續相關性和討論信賴區間的涵蓋關聯。 Zhou (2001)提出了一個可使CVF的絕對值最小的穩健標準，藉由這個準則我們找出了均勻設計在區間[-1,1]之中的最佳實驗順序的一種規則。透過我們提出的方法，我們將重置實驗順序的排列，並說明我們如何將任一組實驗順序的結構區分成三大種類來解決問題。

In this work, a method to choose the best run order for a given experimental design is proposed, for the simple linear regression model with MA errors. More specifically we investigate the best run order of an uniform design when errors follow a MA(1) or a subset MA(k) process where k is a positive integer. The correlation matrix P resulting from the errors is usually difficult to obtain a good estimate. Using the change of variance function(CVF) to see the relation of the uncorrelated and the
serially correlated errors. Criterion proposed by Zhou (2001), we find the best run order of the uniform design on [-1,1] to minimize the robust criterion, |CVF|. We will display the permutation of a run order after rearrangement by our method and show how the structure is decomposed into three categories to solve the problem.

1 Introduction............................................1
1.2 Change of variance function and robust criterion.............................2
2 Robust run order for MA(1) process in the simple linear regression model............. .........................5
3 Robust run order for subset MA process in the simple linear regression model...............................13
3.1 Run order for the subset MA(2) process............14
3.2 Run order for the subset MA(3) process............18
4 Discussions and conclusions.........................24
References............................................25

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