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判别问题中bootstrap与交叉验证误判率估计的偏差和变异AI 解读

Simulation studies have shown that bootstrap and cross-validation estimators of aggregate error rate in discrimination problems have different properties, the former having less variability but greater bias. We show by use of a local alternative model that the main differences in bias and variability emerge only when the populations are close. In this context the bootstrap method has less variability but an order of magnitude greater bias than cross-validation.

一般线性与 SUR 模型中自助法和常规标准误的偏差AI 解读

When estimating the seemingly unrelated regression (SUR) model in small samples, the bootstrap feasible generalized least-squares (FGLS) covariance estimator has been widely advocated as less biased than the conventional FGLS covariance estimator obtained by evaluating the asymptotic covariance matrix. Assuming multivariate normal errors and an unbiased estimator of the error covariance, Eaton proves that the conventional estimator is biased downward for a general SUR model.…

改进的 Berry–Esseen–Chebyshev 界及统计应用AI 解读

A Sharpening Of Nonuniform bounds of the Berry-Esseen type initially obtained by Esseen and later generalized by Kolodjažnyĭ–who also proved that they are, in some sense, optimal–is proposed. Further, the corresponding inequalities are shown to provide uniformly improved Chebyshev bounds for the tail probabilities of the distribution functions to be approximated. In contrast with most results on Berry–Esseen bounds, which emphasize rates of convergence to normality, the…

收入效应矩阵正定性的 Bootstrap 检验AI 解读

Positive definiteness of income effect matrices provides a sufficient condition for the law of demand to hold. Given cross section household expenditure data, empirical evidence for the law of demand can be obtained by estimating such matrices. Härdle, Hildenbrand, and Jerison used the bootstrap method to simulate the distribution of the smallest eigenvalue of random matrices and to test their positive definiteness. Here, theoretical aspects of this bootstrap test of…

用自助法辅助选择向量时间序列的近似表示AI 解读

In this article, a procedure is presented to use the bootstrap in choosing the best approximation in terms of forecasting performance for the equivalent state-space representation of a vector autoregressive model. It is found that the proposed procedure, which uses each approximator's forecasting performance, can enhance considerably an approach based simply on the estimated Hankel singular values.

重抽样方法的效率与稳健性AI 解读

It is known that the standard delete-1 jackknife and the classical bootstrap are in general equally efficient for estimating the mean-square-error of a statistic in the i.i.d. setting. However, this equivalence no longer holds in the linear regression model. It turns out that the bootstrap is more efficient when error variables are homogeneous and the jackknife is more robust when they are heterogeneous. In fact, we can divide all the commonly used resampling procedures for…

核谱估计的自助法AI 解读

An approach to bootstrapping kernel spectral density estimates is described which is based on resampling from the periodogram of the original data. We show that it is asymptotically valid under suitable conditions, and we illustrate its performance for a medium-sized time series sample with a small simulation study.

风险与生存分析中特定发生／暴露率的非参数估计AI 解读

A cohort of individuals exposed to some risk is followed up to a point of time M, and observations on two random variables (Y, Δ) are recorded for each individual. The variable Δ refers to one of the four possible events that can occur for an individual in the period [0, M]: (i) dies of a specific disease, say cancer, (ii) dies of a natural cause, (iii) withdraws from the study, and (iv) is alive and still under study at time M. The variable Y refers to the time at which an…

摘要暂缺

利用次序统计量伴随变量估计分布：自助法 Monte Carlo 模拟应用AI 解读

SUMMARY We show that a simulation method suggested by Efron for approximating bootstrap distributions is closely related to techniques based on concomitants of order statistics and develop its asymptotic properties from that viewpoint. We prove that the method produces Monte Carlo approximations with variance and mean-squared error decreasing like B− 1 n− 1/2, where B denotes the number of simulations and n equals the sample size. Therefore Efron's method can be a competitor…

Geary–Khamis 购买力平价与国际价格标准误的计算：随机方法AI 解读

One of the areas receiving little attention in the past in index-number theory is providing standard errors for the index number estimates. Recently, Clements and Izan and Selvanathan used the stochastic approach to index numbers to derive standard errors for the rate of inflation and Laspeyres and Paasche index numbers. In this article, we use this approach to compute standard errors associated with purchasing power parities computed using Geary-Khamis aggregation procedure…

对模型选择全过程进行自助法推断：一个计量经济学例子AI 解读

Abstract If a researcher has mined the data (i.e. selected an empirical model based on a series of trial estimates), inferences based on the final set of results are in general incorrect. This note treats the entire data mining process as an estimator and shows how a bootstrapping technique may improve the quality of inference. The method is applied to an empirical example on the deterrent effects of capital punishment.

捕获概率异质的再捕获实验：修正鞅估计AI 解读

An estimation method of Lloyd & Yip (1991), based on martingales and the assumption of beta distributed capture probabilities, is modified to improve its performance for all but highly heterogeneous populations. This estimator is compared to the jackknife estimator by simulation under both beta and non-beta conditions. Some expressions for standard error are developed but found to behave poorly for realistic sample sizes. Bootstrap estimates of standard error appear superior…

快速且准确的近似双重自助法置信区间AI 解读

We propose two new methods for the construction of approximate iterated bootstrap confidence intervals. Our methods follow a saddlepoint approach, but employ approximate rather than exact solutions to the nonlinear saddlepoint equations that arise in applying that technique. The main advantages of the new techniques are that they yield confidence intervals with high coverage accuracy in small- to moderately-sized samples and that they achieve this accuracy with very…

判别问题中 bootstrap 与交叉验证误差率估计的偏差和变异性AI 解读

Simulation studies have shown that bootstrap and cross-validation estimators of aggregate error rate in discrimination problems have different properties, the former having less variability but greater bias. We show by use of a local alternative model that the main differences in bias and variability emerge only when the populations are close. In this context the bootstrap method has less variability but an order of magnitude greater bias than cross-validation.

摘要暂缺

非参数回归中野生自助法的收敛速度AI 解读

This paper concerns the distributions used to construct confidence intervals for the regression function in a nonparametric setup. Some rates of convergence for the normal limit, its plug-in approach and the wild bootstrap are obtained conditionally on the explanatory variable $X$ and also unconditionally. The bound found for the wild bootstrap approximation is slightly better (by a factor $n^{-1/45}$) than the bounds given by the plug-in approach or the CLT for the…

正态化变换与 Bootstrap 置信区间AI 解读

This paper considers the problem of constructing approximate confidence intervals for functional parameters in the nonparametric case. The approach based on transformation theory is applied to improve standard confidence intervals. The accelerated bias-corrected percentile interval introduced by Efron relies on the existence of a normalizing transformation with bias and skewness corrections, although calculation does not require explicit knowledge of its functional form. We…

线性模型的经验似然AI 解读

Empirical likelihood is a nonparametric method of inference. It has sampling properties similar to the bootstrap, but where the bootstrap uses resampling, it profiles a multinomial likelihood supported on the sample. Its properties in i.i.d. settings have been investigated in works by Owen, by Hall and by DiCiccio, Hall and Romano. This article extends the method to regression problems. Fixed and random regressors are considered, as are robust and heteroscedastic…

具有相关自相关随机效应的混合模型系统的经验贝叶斯分析AI 解读

Empirical Bayes concepts are implemented in a simultaneous analysis of a system of mixed linear models having linked and serially correlated random effects. Emphasis is placed on the estimation of the random effects and exploration of the relationships between them. Application is made to the investigation of several series of laboratory assay data that were observed during overlapping time intervals and were therefore subjected to common systematic errors, or “daily…

置换检验功效蒙特卡洛模拟中的计算投入分配AI 解读

Consider a randomization test in which an observed statistic is compared to a null distribution constructed by first drawing a random sample from the set of all possible permutations of the data and then calculating the statistic anew for each member of the random sample. If the power of such a test is investigated by simulation, the computer code must have two main loops. In the outer loop, which has O iterations, data are generated under a specific alternative hypothesis.…

状态空间模型的自助法：高斯最大似然估计与卡尔曼滤波AI 解读

The bootstrap is proposed as a method for assessing the precision of Gaussian maximum likelihood estimates of the parameters of linear state-space models. Our results also apply to autoregressive moving average models, since they are a special case of state-space models. It is shown that for a time-invariant, stable system, the bootstrap applied to the innovations yields asymptotically consistent standard errors. To investigate the performance of the bootstrap for finite…

置换检验功效模拟中的计算资源分配AI 解读

Consider a randomization test in which an observed statistic is compared to a null distribution constructed by first drawing a random sample from the set of all possible permutations of the data and then calculating the statistic anew for each member of the random sample. If the power of such a test is investigated by simulation, the computer code must have two main loops. In the outer loop, which has O iterations, data are generated under a specific alternative hypothesis.…

具有相联系自相关随机效应的混合模型系统的经验贝叶斯分析AI 解读

Empirical Bayes concepts are implemented in a simultaneous analysis of a system of mixed linear models having linked and serially correlated random effects. Emphasis is placed on the estimation of the random effects and exploration of the relationships between them. Application is made to the investigation of several series of laboratory assay data that were observed during overlapping time intervals and were therefore subjected to common systematic errors, or “daily…