藉由選取樣本集合的映射之統計推論

Abstract

在這篇論文裡，我們介紹一個觀念：嘗試利用一個一致的方法，去評估各種統計推論問題的所有方法。而對於每個推論方法，我們可定義一個函數，將此推論方法映射到樣本空間的一個子集。當他們被應用於評量統計推論方法的好壞時，我們可以藉由映射子集之大小來評估，因此我們可以訂定各種不同計算大小的標準，去評量一個方法的好壞。對於映射子集大小的標準，我們可以採用的標準含映射集合的體積，映射集合的變異和映射集合的密度大小。在這篇論文裡我們會藉由一些例子，來討論這些標準的應用。

Our aim in this paper is to introduce a concept trying to evaluate statistical inference techniques for all statistical inference problems with a unifying method. For each inference problem, we may define a function mapping each inference technique to a subset of the sample space. Then we can define various criterions in evaluating the size of the mapping for all techniques when they are applied for one statistical inference problem. The criterions of the size for the mapping including the volume of the mapping set and probability variation of the mapping set are considered as examples in this paper. We initiate this direction of evaluation of an inference technique in terms of the size of its corresponding mapping set is interesting whereas the use of size in our three methods still needs for further investigation.