Components of X 2 for Testing Distributional Assumptions Against Certain Restricted Alternatives
针对受限备择检验分布假设的 Pearson 卡方分量
Motivated by the problems of detecting skewness and heavy tails in hypothetically normally distributed data, partially ordered families of alternative distributions are developed, the orderings being chosen to reflect skewness and tail weight. Optimal components of Pearson's X2, optimal in a minimax sense for detecting alternatives of this kind, are presented and their properties are discussed. Alternative approaches to the problem are also briefly discussed.