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Lévy 邻域中位置参数 M、R 与 L 估计量的极小极大性质AI 解读

In the context of Huber's theory of robust estimation of a location parameter, the literature on minimax properties of $M$-, $R$- and $L$-estimators is surveyed. New results are obtained for the model in which the unknown error distribution is assumed to lie in a Levy neighbourhood of a symmetric distribution $G: \mathscr{P}_{\varepsilon,\delta}(G) = \{F\mid G(x - \delta) - \varepsilon \leq F(x) \leq G(x + \delta) + \varepsilon \text{for all} x\}$. Under reasonably general…

均值未知时指数分布拟合优度检验的校正AI 解读

Srinivasan (1970) proposed a two-sided Kolmogorov-Smirnov type test for testing the goodness of fit of exponential and normal distributions with parameters unspecified. For the exponential distribution, this test was reported to have surprisingly better power than a similar test proposed by Lilliefors (1969). We show in this paper that the critical values given by Srinivasan (1970) are too low and the power calculations are incorrect. We give the correct critical values for…