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正态分布对双指数备择的最强尺度与位置不变检验AI 解读

The most powerful scale and location invariant test of normality against the double exponential alternative is derived by the technique of integrating with respect to the scale and location transformation group. The resultant test is asymptotically equivalent to the likelihood ratio test of this hypothesis and to Geary's test (i.e. mean deviation over standard deviation) for all three test statistics are shown to have the same asymptotic normal distribution when the sampling…

底层分布的选择与自适应估计AI 解读

In our approach to adaptive inference, selection of the true underlying family of distributions is needed. A Bayesian selection rule, which is based on non-informative priors for the parameters, and a multiple decision solution, that maximizes the weighted sum of the probabilities of correct selection, are presented; both of these yield a decision rule of the same form. A modified maximum likelihood solution is also given and is used to construct an adaptive estimate of the…