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对称中心未知时的对称分布函数估计
This paper considers the problem of estimating the distribution function of a symmetric distribution when the centre of symmetry is unknown. An estimator is proposed which is shown to be asymptotically better than the empirical distribution function for well-known distributions including the normal, double exponential and Cauchy.
基于 Kolmogorov–Smirnov 统计量的位移与对称中心估计
A point estimator and a set of confidence intervals based on the Kolmogorov-Smirnov statistic are proposed for the shift parameter in the two-sample problem. Asymptotic distibution of the etimator as well as asymptotic bounds for the lengths of the intervals are derived. The two-sample results are then adapted to the one-sample problem to define an estimator and a set of confidence intervals for the center of a symmetric population.
对称分布的分布函数估计
This paper considers the problem of estimating the distribution function of a symmetric distribution when the centre of symmetry is unknown. An estimator is proposed which is shown to be asymptotically better than the empirical distribution function for well-known distributions including the normal, double exponential and Cauchy.
连续对称分布的拟合优度检验
This article considers the problem of testing a completely specified continuous symmetric distribution against alternatives which are also symmetric about the same point. The symmetry is utilized in obtaining a new distribution-free statistic of the Kolomogorov-Smirnov type which can be used to halve the width of the Kolomogorov-Smirnov confidence band for the unknown distribution function.