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平滑与自助法AI 解读

Recent attention has focussed on possible improvements in performance of estimators which might flow from using the smoothed bootstrap. We point out that in a great many problems, such as those involving functions of vector means, any such improvements will be only second-order effects. However, we argue that substantial and significant improvements can occur in problems where local properties of underlying distributions play a decisive role. This situation often occurs in…

若干非参数假设的自助法与随机化检验AI 解读

In this paper, the asymptotic behavior of some nonparametric tests is studied in situations where both bootstrap tests and randomization tests are applicable. Under fairly general conditions, the tests are asymptotically equivalent in the sense that the resulting critical values and power functions are appropriately close. This implies, among other things, that the difference in the critical functions of the tests, evaluated at the observed data, tends to 0 in probability.…

参数似然与经验似然函数的比较AI 解读

In this paper, parametric and empirical likelihood functions or surfaces are compared. In particular, first- and second-order expansions for log likelihood functions are developed in nonparametric and parametric situations, where the functional of interest is a smooth function of vector means. The two approaches are compared and the precise order of difference between the nonparametric and parametric log likelihood functions is obtained. In general, the surfaces need not…

基于经验似然比统计量带符号平方根的调整AI 解读

The standard multivariate normal approximation to the distribution of the signed root of the empirical likelihood ratio statistic is considered in cases where inference is required for a smooth function of the mean of the distribution from which the sample is drawn. The error in this approximation is of order O(n−½) where n is the sample size, and it is shown that the error can be reduced to order O(n−1) by using a mean adjustment. When a scalar parameter is of interest, use…

摘要暂缺

自助法置信区间综述AI 解读

SUMMARY A survey of bootstrap procedures for constructing confidence regions is given. In particular, several distinct bootstrap methods are considered, with emphasis on the mathematical correctness of these procedures. The percentile, bias-corrected percentile and accelerated bias-corrected percentile methods, developed by Efron, are reviewed in both parametric and nonparametric situations. A procedure related to the accelerated bias-corrected method, which avoids explicit…

核密度众数估计的弱收敛与最优性AI 解读

A mode of a probability density $f(t)$ is a value $\theta$ that maximizes $f$. The problem of estimating the location of the mode is considered here. Estimates of the mode are considered via kernel density estimates. Previous results on this problem have several serious drawbacks. Conditions on the underlying density $f$ are imposed globally (rather than locally in a neighborhood of $\theta$). Moreover, fixed bandwidth sequences are considered, resulting in an estimate of…

Given a sample from a distribution F supported on a p-dimensional sphere, several confidence cones for the ‘mean directional vector’ are proposed. Some methods have been available, but they depend on parametric assumptions. In this paper, nonparametric confidence cones based on the bootstrap are considered, and consistency of these methods is obtained under minimal conditions. We compare the performances of bootstrap methods with the others by Monte Carlo simulations.