关于拟合优度检验的EDF统计量的若干评注(英语)

拟合优度检验是建立统计模型的一个重要手段,很多检验统计量用一个理想样本能达到它们自己的极值,但EDF统计量做不到,这无疑会影响检验的势。在本文中,我们将提出某些调整型EDF统计量,它们具有这些性质,并改进了EDF检验,蒙得卡罗模拟表明,调整型EDF统计量在很多场合要必EDF具有更高的势,特别对重尾的备选分布更是这样,我们还考察了检验的形态与它们的极值点之间的关系。     

Tests of fit for the Rayleigh distribution based on the empirical Laplace transform

In this paper a class of goodness-of-fit tests for the Rayleigh distribution is proposed. The tests are based on a weighted integral involving the empirical Laplace transform. The consistency of the tests as well as their asymptotic distribution under the null hypothesis are investigated. As the decay of the weight function tends to infinity the test statistics approach limit values. In a particular case the resulting limit statistic is related to the first nonzero component of Neyman’s smooth test for this distribution. The new tests are compared with other omnibus tests for the Rayleigh distribution.     

Towards data driven selection of a penalty function for data driven Neyman tests

The data driven Neyman statistic consists of two elements: a score statistic in a finite dimensional submodel and a selection rule to determine the best fitted submodel. For instance, Schwarz BIC and Akaike AIC rules are often applied in such constructions. For moderate sample sizes AIC is sensitive in detecting complex models, while BIC works well for relatively simple structures. When the sample size is moderate, the choice of selection rule for determining a best fitted model from a number of models has a substantial influence on the power of the related data driven Neyman test. This paper proposes a new solution, in which the type of penalty (AIC or BIC) is chosen on the basis of the data. The resulting refined data driven test combines the advantages of these two selection rules.     

Some test statistics based on the martingale term of the empirical distribution function

Summary It is proved that the martingale term of the empirical distribution function converges weakly to a Gaussian process inD[0, 1]. Some statistics for goodness-of-fit tests based on the martingale term of the empirical distribution function are proposed. Asymptotic distributions of these statistics under the null hypothesis are given. The approximate Bahadur efficiencies of the statistics to the Kolmogorov-Smirnov statistic and to the Cramér-von Mises statistic are also calculated. The Institute of Statistical Mathematics