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检验单个协方差矩阵结构的稳健方法AI 解读

Patterns for a single covariance matrix may be studied using likelihood ratio or quadratic form test statistics. Typically these tests have an asymptotic chi-squared distribution when the data are normally distributed, but the asymptotic distribution is sensitive to nonnor-mality. This paper suggests two ways to robustify inference for patterned matrices: (i) estimate the critical values of normal theory test statistics using a new bootstrap procedure which takes advantage…

利用非参数曲线进行模型检验AI 解读

The use of local likelihood curve estimates in model checking is described. Test statistics are based on deviance differences, and are interpreted using nonparametric bootstrap Monte Carlo. Some theoretical aspects are discussed. Methods are illustrated for regression with discrete data.

学生化均值的鞍点近似及其自助法应用AI 解读

A saddlepoint technique is used to approximate to the density and tail probability of the studentized mean of a random sample. The motivation was to replace bootstrapping of the studentized mean in the way Davison & Hinkley (1988) used the saddlepoint approximation for the unstudentized mean. The method involves first obtaining a bivariate saddlepoint approximation, then, after a nonlinear transformation, integrating out an unwanted variable either numerically or by a…

自助法中的重要性重抽样AI 解读

We introduce an empirical method of importance resampling, which does not require analytical calculation of the resampling probabilities. Our method can easily be used as part of a general algorithm for Monte Carlo calculation of bootstrap confidence intervals and hypothesis tests. It produces consistent, efficient and unbiased Monte Carlo approximations. We also present a very general but elementary account of importance resampling, which shows that even optimal importance…

两种药物独立联合作用检验的大样本性质AI 解读

Biological models for the independent action of two drugs imply that if the drugs are administered in various combinations of doses, then the corresponding probabilities of response must satisfy certain inequalities if the drugs are acting independently. The hypothesis that the probabilities do satisfy these inequalities can be tested using the likelihood ratio test or using the bootstrap test proposed by Wahrendorf and Brown in 1980. In the simplest dose design, only one…

核密度估计的自助法带宽选择AI 解读

A bootstrap-based choice of bandwidth for kernel density estimation is introduced. The method works by estimating the integrated mean squared error (IMSE) for any given bandwidth and then minimizing over all bandwidths. A straightforward application of the bootstrap method to estimate the IMSE fails because it does not capture the bias component. A smoothed bootstrap method based on an initial density estimate is described that solves this problem. It is possible to…

置信区间覆盖率校正中的自助法迭代AI 解读

Iterated bootstrap procedures may be used to reduce error in many statistical problems. We discuss their use in constructing confidence intervals with accurate coverage and show that bootstrap coverage correction produces improvements in coverage accuracy of order n −1/2 in one-sided intervals, but of order n −1 in two-sided intervals. Explicit formulas are provided for the dominant term in coverage error after iteration in each case. These results are used to compare…

非参数回归中均值函数差异的 Bootstrap 检验AI 解读

A bootstrap test is proposed for detecting a difference between two mean functions in the setting of nonparametric regression. Error distributions in the regression model are permitted to be arbitrary and unequal. The test enjoys power properties akin to those in a parametric setting, in the sense that it can distinguish between regression functions distant only n −1/2 apart, where n is the sample size. It has exceptional level accuracy, with level error of only n −2, and…

通过自助法迭代校正置信区间覆盖率AI 解读

Iterated bootstrap procedures may be used to reduce error in many statistical problems. We discuss their use in constructing confidence intervals with accurate coverage and show that bootstrap coverage correction produces improvements in coverage accuracy of order n −1/2 in one-sided intervals, but of order n −1 in two-sided intervals. Explicit formulas are provided for the dominant term in coverage error after iteration in each case. These results are used to compare…

Bootstrap模拟的平衡设计AI 解读

SUMMARY Davison et al. (1986) have shown that finite bootstrap simulations can be improved by forcing balance in the aggregate of simulated data sets. Their methods yield first-order balance, which principally affects bootstrap estimation of bias. Here we extend the methodology to second-order balance, which principally affects bootstrap estimation of variance. The particular techniques involve Latin square and balanced incomplete block designs. Numerical examples are given…

预测区域的校准AI 解读

Suppose that the variable X to be predicted and the learning sample Yn that was observed have a joint distribution, which depends on an unknown parameter θ. The parameter θ can be finite- or infinite-dimensional. A prediction region Dn for X is a random set, depending on Yn , that contains X with prescribed probability α. This article studies methods for controlling simultaneously the conditional coverage proability of Dn , given Yn , and the overall (unconditional) coverage…

缺少群不变性假设时随机化检验的表现AI 解读

Fisher's randomization construction of hypothesis tests is a powerful tool to yield tests that are nonparametric in nature in that their level is exactly equal to the nominal level in finite samples over a wide range of distributional assumptions. For example, the usual permutation t test to test equality of means is valid without a normality assumption of the underlying populations. On the other hand, Fisher's randomization construction is not applicable in this example…

平滑 Bootstrap 的替代方法AI 解读

SUMMARY Bootstrap estimation of simple population functionals is considered. The smoothed bootstrap (Efron, 1979, 1982) is compared with an alternative estimation procedure based on resampling ideas of Kendall and Kendall (1980). Specific examples of the estimation problem are considered, showing that the competing estimators may display different qualitative behaviours.

小样本置信区间AI 解读

In this article we present a technique for constructing one- or two-sided confidence intervals, which are second-order correct in terms of coverage, for either parametric or nonparametric problems. The construction is valid in the presence of nuisance parameters. The situation we consider is this: there are p parameters and we want a confidence interval for some function of them, possibly one of the parameters itself. The p parameters are estimated by M-estimates, which…

Bootstrap 同时置信集的改进AI 解读

Simultaneous confidence sets for a collection of parametric functions may be constructed in several different ways. These ways include: (a) the exact pivotal method that underlies Tukey's (1953) and Scheffé's (1953) simultaneous confidence intervals for linear parametric functions in the normal linear model; (b) the method of asymptotic pivots, which is an approximate extension of the pivotal method; (c) the method of bootstrapped roots developed in Beran (1988). These three…

摘要暂缺

用自助法构造置信区间：多产品成本函数的应用AI 解读

A multi-product cost function system is estimated for 387 banks in states that allow branch banking. The bootstrap resampling method is used to construct confidence intervals for marginal costs, output-cost elasticities, economies of scale and scope, and Allen elasticities of substitution. Confidence intervals for these measures are usually constructed using a first-order variance approximation under a normality assumption, but such confidence intervals are inexact if the…

摘要暂缺

The small-sample behavior of the bootstrap is investigated as a method for estimating p values and power in the stationary first-order autoregressive model. Monte Carlo methods are used to examine the bootstrap and Student-t approximations to the true distribution of the test statistic frequently used for testing hypotheses on the underlying slope parameter. In contrast to Student's t, the results suggest that the bootstrap can accurately estimate p values and power in this…

一阶自回归中 p 值与检验力的自助法估计：蒙特卡洛研究AI 解读

The small-sample behavior of the bootstrap is investigated as a method for estimating p values and power in the stationary first-order autoregressive model. Monte Carlo methods are used to examine the bootstrap and Student-t approximations to the true distribution of the test statistic frequently used for testing hypotheses on the underlying slope parameter. In contrast to Student's t, the results suggest that the bootstrap can accurately estimate p values and power in this…

交叉验证、贝叶斯定理与小样本偏差AI 解读

Researchers in many fields of business are beginning to use cross-validatory techniques to choose between alternative models. In marketing, a Bayesian interpretation of the technique has been proposed. This article examines the Bayesian link in more detail and shows that cross-validatory posterior odds exhibit a systematic departure from exact posterior odds when sample-splitting procedures are employed. Resampling procedures also exhibit a systematic departure when the…

Bootstrap偏差AI 解读

Use of the bootstrap in estimation of the sampling distribution of a pivot is considered for two simple situations. It is shown by a simulation study that in each case the bootstrap is noticeably biased for small sample sizes. The techniques of computer algebra are used to obtain an exact assessment of the bias in both problems and an approximate theoretical analysis based on saddlepoint approximation is presented.

截断时间与失效时间独立性假设的检验AI 解读

For data subject to random censorship, it is well known that the assumption of independence between censoring time and failure time cannot be tested nonparametrically. For data subject to random truncation, however, it is possible to test independence of truncation time and failure time. A statistic generalizing Kendall's tau is proposed for testing the independence assumption, and asymptotic properties under the null hypothesis are derived. A conditional permutation test is…

经验似然的伪似然理论AI 解读

It is proved that, except for a location term, empirical likelihood does draw contours which are second-order correct for those of a pseudo-likelihood. However, except in the case of one dimension, this pseudo-likelihood is not that which would commonly be employed when constructing a likelihood-based confidence region. It is shown that empirical likelihood regions may be adjusted for location so as to render them second-order correct. Furthermore, it is proved that…