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最大似然估计的序贯置信域AI 解读

The goal of this paper is to develop a general framework for constructing sequential fixed size confidence regions based on maximum likelihood estimates. Asymptotic properties of the sequential procedure for setting up the confidence regions are analyzed under very broad assumptions on the underlying parametric model. It is shown that the proposed sequential procedure is asymptotically optimal in the sense that it approximates the optimal fixed-sample size procedure. It is…

P{X<Y} 的最小方差无偏估计量的容许性与极小极大性AI 解读

Suppose that $X_1,\ldots, X_m$ are i.i.d. from a continuous distribution function $F$ and $Y_1,\ldots, Y_n$ are i.i.d. from a continuous distribution function $G; X$'s and $Y$'s are independent. A minimum variance unbiased estimator of $P\{X < Y\}$ is the Mann-Whitney statistic. We show that the Mann-Whitney statistic is admissible under a class of weighted squared error losses and is minimax under a proper weighted squared error loss.

针对自相关正态备择的随机性非参数检验AI 解读

Locally most powerful rank tests of randomness against autocorrelated normal alternatives are derived. In particular, autoregressive and moving average alternatives are considered. The distribution of the statistic under the hypothesis of randomness is shown to be asymptotically normal. The small sample power of the test procedure is compared with that of two other procedures by the Monte Carlo Method.

针对自相关正态备择的随机性非参数检验AI 解读

Locally most powerful rank tests of randomness against autocorrelated normal alternatives are derived. In particular, autoregressive and moving average alternatives are considered. The distribution of the statistic under the hypothesis of randomness is shown to be asymptotically normal. The small sample power of the test procedure is compared with that of two other procedures by the Monte Carlo Method.

正态总体混合下 Stein 两阶段程序的稳健性AI 解读

Explicit expressions for the level of significance and power of Stein's two-stage hypothesis testing procedure are derived when the normal population is mixed with another normal population differing in the mean. Approximate expansions for these expressions have been obtained, and numerical studies of the size have been carried out using the expansions. Some numerical indication of the accuracy of the approximations has also been obtained. Stein's two-stage procedure is…

Stein 两阶段程序对正态总体混合的稳健性AI 解读

Explicit expressions for the level of significance and power of Stein's two-stage hypothesis testing procedure are derived when the normal population is mixed with another normal population differing in the mean. Approximate expansions for these expressions have been obtained, and numerical studies of the size have been carried out using the expansions. Some numerical indication of the accuracy of the approximations has also been obtained. Stein's two-stage procedure is…

若干单样本序贯秩检验的停止时间AI 解读

Two models for modified, one-sample, sequential probability ratio tests based on Lehmann alternatives are considered, one developed by Weed and Bradley and one by Govindarajulu. It is shown how they are related. Sure termination of the SPRT's is established under very general conditions.

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