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污染情形下最小对比估计量的中偏差AI 解读

Since statistical models are simplifications of reality, it is important in estimation theory to study the behavior of estimators also under distributions (slightly) different from the proposed model. In testing theory, when dealing with test statistics where nuisance parameters are estimated, knowledge of the behavior of the estimators of the nuisance parameters is needed under alternatives to evaluate the power. In this paper the moderate deviation behavior of minimum…

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功效差距趋零与渐近相对效率AI 解读

The shortcoming of a test is the difference between the maximal attainable power and the power of the test under consideration. Vanishing shortcoming, when the number of observations tends to infinity, is therefore an optimality property of a test. Other familiar optimality criteria are based on the asymptotic relative efficiency of the test. The relations between these optimality criteria are investigated. It turns out that vanishing shortcoming is seemingly slightly…

复合假设的数据驱动光滑检验AI 解读

The classical problem of testing goodness-of-fit of a parametric family is reconsidered. A new test for this problem is proposed and investigated. The new test statistic is a combination of the smooth test statistic and Schwarz's selection rule. More precisely, as the sample size increases, an increasing family of exponential models describing departures from the null model is introduced and Schwarz's selection rule is presented to select among them. Schwarz's rule provides…

数据驱动 Neyman 均匀性检验的渐近最优性AI 解读

Data-driven Neyman's tests resulting from a combination of eyman' smooth tests for uniformity and Schwarz's selection procedure are nvestigated. Asymptotic intermediate efficiency of those tests with respect to the Neyman-Pearson test is shown to be 1 for a large set of converging alternatives. The result shows that data-driven Neyman's tests, contrary to classical goodness-of-it tests, are indeed omnibus tests adapting well to the data at hand.

Kolmogorov–Smirnov、Cramér–von Mises 与卡方统计量的过度偏离概率AI 解读

Let $\alpha_n$ be the classical empirical process and $T: D\lbrack 0, 1\rbrack \rightarrow R$. Assume $T$ satisfies the Lipschitz condition. Using the Komlos-Major-Tusnady inequality, bounds for $P(T(\alpha_n) \geq x_n \sqrt n)$ are obtained for every $n$ and $x_n > 0$. Hence expansions for large deviations, as well as some moderate and Cramer-type large-deviations results for $T(\alpha_n)$, are derived.