在迴歸分析中，常常有不同的模式假設及相對應的分析方法，也時常可以見到同樣的模式有2種以上的估計方法，一般並不知道在何種資料型態上何種估計方法孰優孰劣。要選用何種估計方法，取決於資料的分佈，而資料分佈又如何決定何種估計法較優，通常是無法事先知道的。當我們不清楚何種資料應使用何種估計方式較佳時，可能會使用了較沒效率的方法造成估計結果變異較大。為了降低這種風險，本文提出了無母數的合併估計方法，找出一個適合的比例，讓資料自動偏向較有效率的估計方法，且本文所探討的方法，在分配或迴歸函數形式的假設要求並不多，很容易應用在各種實驗資料的估計。最後我們利用電腦模擬的方法來比較各種估計法的表現，計算平均估計值、變異數與95%信賴區間涵蓋率，並對結果加以討論。

In regression analysis,there are usually more than one estimation approaches for one model hypothesis.In general,which approach is better for a certain pattern of data is unknown.The determination of estimation approaches depends on distributions of data,and the distribution itself decides which approach is better.If the better approach for the corresponding data is not clear,the less efficient approach might be chosen and expand the variance.We propose an estimating method of nonparametrical combination to decrease the risk,a method to find out an appropriate proportion that help we conclude a more effective method.Besides,the method doesn't require a lot of assumptions on distributions or forms of regression functions,therefore it can be applied in estimations of different kinds of experiment data.Finally we compare the performance between estimation methods by calculating average estimated numbers,variances,and 95% confidence interval coverage percent through computer simulations,and the result is discussd.

1緒論..................................................1  
2線性及廣義線性模式中有測量誤差時的各2種估計方法.......3
 2.1 線性迴歸模式中的2種估計方法.......................3
 2.2 廣義線性模式中有測量誤差時的2種估計方法...........5
3無母數的合併估計方法..................................9
 3.1 以分組估計相關性..................................11
 3.2 以拔靴法重抽估計..................................14
4模擬實驗..............................................16
 4.1模擬分析...........................................16
 4.2模擬結果...........................................17
5結論..................................................18
參考文獻...............................................19
圖表目錄...............................................20
表1-1..................................................20
圖(a)..................................................20
表1-2..................................................21
圖(b)..................................................21
表2-1..................................................22
表2-2..................................................22

Fuller, W. A. (1980).Properties of some estimators for the errors in variables model. Annals of Statistics, 8, 407-422.

Fuller, W. A.(1987). Measurement Error Models. John Wiley & Sons, New York.

McCullagh, P. & Nelder,J. A. (1989). Generalized Linear Models, second edition. Chapman & Hall, London.

Measurement Error in Nonlinear Models R.J. Carroll, D. Ruppert and L.A. Stefanski(1995)

Nakamura, T. (1990) Corrected score functions for errors-in-variables models:methodology and application to generalized linear models.Biometrika,77, 127-137.

Stefanski, L. A. (1989). Unbiased estimation of a nonlinear function of a normal mean with application to measurement error models.Communications in Statistics, Series A, 18, 4335-4358.

Stefanski, L. A. and Carroll R. J. (1987). Conditional scores and Optimal scores for generalized linear measurement-error models. Biometrika 74, 703-716.

Yadolah Dodge and Jana Jureckova(2000). Adaptive Regression.