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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…

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…

预检验程序的检验尺寸与功效AI 解读

A pretest procedure consists of a preliminary test on a nuisance parameter, investigating whether it equals a given value or not, followed by the main testing problem on the parameter of interest. In case of acceptance of the preliminary test, the main test is applied in the restricted family with the given value of the nuisance parameter, while otherwise the test is performed in the complete family, including the nuisance parameter. For an appropriate class of tests,…

数据驱动的独立性秩检验AI 解读

We introduce new rank tests for testing independence. The new testing procedures are sensitive not only for grade linear correlation, but also for grade correlations of higher-order polynomials. The number of polynomials involved is determined by the data. Model selection is combined with application of the score test in the selected model. Whereas well-known tests as Spearman's test or Hoeffding's test may completely break down for alternatives that are dependent but have…

复合假设下的数据驱动光滑检验AI 解读

In recent years several authors have recommended smooth tests for testing goodness of fit. However, the number of components in the smooth test statistic should be chosen well; otherwise, considerable loss of power may occur. Schwarz's selection rule provides one such good choice. Earlier results on simple null hypotheses are extended here to composite hypotheses, which tend to be of more practical interest. For general composite hypotheses, consistency of the data-driven…

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…

数据驱动平滑拟合优度检验的一致性与蒙特卡洛模拟AI 解读

The data driven method of selecting the number of components in Neyman's smooth test for uniformity, introduced by Ledwina, is extended. The resulting tests consist of a combination of Schwarz's Bayesian information criterion (BIC) procedure and smooth tests. The upper bound of the dimension of the exponential families in applying Schwarz's rule is allowed to grow with the number of observations to infinity. Simulation results show that the data driven version of Neyman's…

局部与非局部效率度量AI 解读

General results on the limiting equivalence of local and nonlocal measures of efficiency are obtained. Why equivalence occurs in so many testing and estimation problems is clarified. Uniformity of the convergence is a key point. The concepts of Frechet- and Hadamard-type differentiability, which imply uniformity, play an important role. The theory is applied to tests based on linear rank statistics, showing equivalence of the local limit of exact Bahadur efficiency and…

估计中的中偏差理论AI 解读

The performance of a sequence of estimators $\{T_n\}$ of $\theta$ can be measured by the probability concentration of the estimator in an $\varepsilon_n$-neighborhood of $\theta$. Classical choices of $\varepsilon_n$ are $\varepsilon_n = cn^{-1/2}$ (contiguous case) and $\varepsilon_n = \varepsilon$ fixed for all $n$ (non-local case). In this article all sequences $\{\varepsilon_n\}$ with $\lim_{n\rightarrow\infty} \varepsilon_n = 0$ and $\lim_{n\rightarrow\infty} \varepsilon_nn^{1/2} = \infty$…

Chernoff 效率与亏损AI 解读

In 1952 Chernoff introduced a measure of asymptotic efficiency for tests. Comparison in the sense of Chernoff is concerned with fixed alternatives. In contrast to Bahadur's approach, where the probabilities of first and second kind are treated in an unbalanced way, in Chernoff's approach both probabilities go to zero. For the calculation of Chernoff efficiencies one has to develop large deviation theorems both under the null hypothesis and under the alternative hypothesis.…