Large Sample Theory of Spacings Statistics for Tests of Fit for the Composite Hypothesis
研究了在复合原假设和邻近备择假设下，基于样本间距的非对称函数的检验的大样本理论，并构造了该类中的最优拟合优度检验。
SUMMARY Let X 1,…, Xn be a sequence of independent and identically distributed random variables with an unknown underlying continuous cumulative distribution function F. Often we would like to test a null hypothesis concerning the goodness of fit of F to some distribution function which is fully specified or belongs to some parametric family, i.e. in some applications the null hypothesis is simple whereas in others it may be composite. In this paper we present the large sample theory of tests based on non-symmetric functions of sample spacings under composite null hypotheses as well as under contiguous alternatives. Goodness-of-fit tests which are optimal within this class are constructed.