Can We Bootstrap Even if CLT Fails?

It is shown that in some cases the bootstrap in probability holds under conditions weaker than necessary for the original empirical Central Limit Theorem.     

A Note on the Strong Approximation of the Smoothed Empirical Process of α-mixing Sequences

A strong approximation of the smoothed empirical process of strictly stationary α-mixing random variables by a sequence of iid Gaussian processes will be studied. Here, the smoothing is done via kernel density estimators. No assumptions are made on the support of the kernel; in fact, our main results are stated for kernels with possibly an infinite support. Received June 2003; Accepted February 2004.     

Bootstrap techniques in semiparametric estimation methods for ARFIMA models: A comparison study

Summary  This paper considers different bootstrap procedures for investigating the estimation of the fractional parameter d in a particular case of long memory processes, i.e. for ARFIMA models withd in (0.0, 0.5). We propose two bootstrap techniques to deal with semiparametric estimation methods of d. One approach consists of the local bootstrap method for time frequency initially suggested for the ARMA case by Paparoditis and Politis (1999), and the other consists of the bootstrapping in the residuals of the frequency-domain regression equation. Through Monte Carlo simulation, these alternative bootstrap methods are compared, based on the mean and the mean square error of the estimators, with the well-known parametric and nonparametric bootstrap techniques for time series models.     

The bootstrap: Some large sample theory and connections with robustness

The bootstrap, discussed by Efron (1979, 1981), is a powerful tool for the nonparametric estimation of sampling distributions and asymptotic standard errors. We demonstrate consistency of the bootstrap distribution estimates for a general class of robust differentiable statistical functionals. Our conditions for consistency of the bootstrap are variants of previously considered criteria for robustness of the associated statistics. A general example shows that, for almost any location statistic, consistency of the bootstrap variance estimator requires a tail condition on the distribution from which samples are taken. A modification of Efron's estimator of standard error is shown to circumvent this problem.     

线性相关模型中误差方差的经验似然估计及其Bootstrap

该文利用经验似然方法，对线性相关模型中误差方差的传统最小二乘型估计进行修正，得到的修正估计其渐近方差比传统估计的更小．同时，我们还讨论了修正估计的Bootstrap逼近问题．关键词##4相关模型;;误差方差;;最小二乘;;经验似然;;Bootstrap．     

On the Local Time of the Weighted Bootstrap and Compound Empirical Processes

This article is mainly concerned with the local times of the weighted bootstrap process. We prove a strong approximation theorem for the local time of the weighted bootstrap process by the local time of a Brownian bridge. We consider also the local time of the compound empirical processes that can be seen, asymptotically, as the local time of the convolution of two independent Gaussian processes.     

Behaviour in small samples of some tests of non-nested hypotheses in non-stationary regressions and their bootstrap versions

Summary  In this paper, we use simulation methods to assess, in small samples, the performance of the Davidson and MacKinnon (1981) J-test when it is used to discriminate between two non-nested models with non-stationary regressors. We distinguish two cases: first, we assume that the sets of regressors of the two models are cointegrated; secondly, we consider the case where the regressors are not cointegrated. We also compare the behaviour of this test with that of the Fisher McAleer JA-type test and the bootstrap-adjusted J-tests, in order to assess its relative performance.     

On a One-Parameter Generalization of the Brownian Bridge and Associated Quadratic Functionals

A one-parameter generalization of the Brownian bridge is studied. These processes are then used to compute the laws of some quadratic functionals of Brownian motion, and to obtain identities in law involving local time of modified Bessel processes up to their first hitting time.     

Review of Some Functionals of Compound Poisson Processes and Related Stopping Times

The paper reviews recent results of D. Perry, W. Stadje and S. Zacks, on functionals of stopping times and the associated compound Poisson process with lower and upper linear boundaries. In particular, formulae of these functionals are explicitly developed for the total expected discounted cost of discarded service in an M/G/1 queue with restricted accessibility; for the expected total discounted waiting cost in an M/G/1 restricted queue; for the shortage, holding and clearing costs in an inventory system with continuous input; for the risk in sequential estimation and for the transform of the busy period when the upper boundary is random.      

联合检测过程位置参数和尺度参数的非参数Cusum控制图

用于检测生产过程的多数传统控制图都假定过程的受控分布是已知的,并假定数据服从正态分布。然而在很多情况下,由于没有足够的数据来估计过程的分布,这种假定就变得不现实,而非参数控制图却不需要任何关于分布的特殊形式的假定。另外,多数的已有控制图都是使用两个单独的均值与方差控制图来同时检测生产过程.本文中,我们提出一个新的基于Cramer-von-Mises(CvM)检验的非参数累积和控制图(称为CvM图)来同时检测过程位置参数和尺度参数。文中给出了基于不同受控平均运行长度(ARL)下的CvM图的控制限,通过步长的均值、方差及分位数来研究控制图的性能表现。最后用一个实例来说明CvM图的实际应用。     

On the Maximum of Some Conditional and Integrated Gaussian Fields and their Statistical Applications

We evaluate upper bounds for the maximal distributions of some Gaussian random fields, which arise in the study of the asymptotic behavior of various two-dimensional empirical processes, with random index. Some of them are generalizations of well-known conditional Brownian fields, while the others are obtained by their integration. We present also some possible statistical applications of our results.