建立在伽瑪散度下穩健模型的調整參數之選取

Abstract

Windham在1995年的論文Robustifying Model Fitting提出權重分布方法，解決在存有異常數據情況下可有效的估計均值，這個權重分布使用了一個參數，這個參數會影響到均值的估計表現。Windham同時提出此參數的選取方法，但我們發現在一些數值模擬例子中，這個參數選取方法表現並不佳。我們提出另一個選取方法，在數值模擬上有較佳的表現。除了一般的均值估計，我們也成功地把此方法應用在群聚分析。

In 1995, Windham came out with an idea of weighted distribution in his thesis, Robustifying Model Fitting, and he used the idea to find a mean estimator when there are outliers in the original data. There is a tuning parameter in this estimator, and selecting the parameter will affect the mean estimate in the same data. In the same thesis, he also suggested a criterion of selecting the tuning parameter, but we found out that this criterion wasn’t doing well in some simulations. Considering the problem, we propose another criterion which can derive a better mean estimator. Besides, we can also apply this method to clustering problem.