The introduction of our paper discusses the leave-one-out and cross-validation error estimators. In our implementation of cross-validation, we use k = 5 folds and 5 repetitions, each with different partitions. The basic bootstrap zero estimator, ε̂b0, [3], [4] generates B bootstrap samples, each consisting of n equally-likely draws with replacement from the original sample of size n. Each bootst...

SUMMARY This paper first provides a critical review on some existing methods for estimating prediction error in classifying microarray data where the number of genes greatly exceeds the number of specimen. Special attention is given to the bootstrap-related methods. When the sample size n is small, we find that all the reviewed methods suffer from either substantial bias or variability. We intr...

8 Efron (1979) introduced the bootstrap method for independent data but it can not be easily applied to spatial data because of their dependency. For spatial data that are correlated in terms of their locations in the underlying space the moving block bootstrap method is usually used to estimate the precision measures of the estimators. The precision of the moving block bootstrap estimators is ...

We study the validity of the pairs bootstrap for Lasso estimators in linear regression models with random covariates and heteroscedastic error terms. We show that the naive pairs bootstrap does not consistently estimate the distribution of the Lasso estimator. In particular, we identify two different sources for the failure of the bootstrap. First, in the bootstrap samples the Lasso estimator f...

8 Efron (1979) introduced the bootstrap method for independent data but it can not be easily applied to spatial data because of their dependency. For spatial data that are correlated in terms of their locations in the underlying space the moving block bootstrap method is usually used to estimate the precision measures of the estimators. The precision of the moving block bootstrap estimators is ...

The m out of n bootstrap Bickel et al. [1997], Politis and Romano [1994] is a modification of the ordinary bootstrap which can rectify bootstrap failure when the bootstrap sample size is n. The modification is to take bootstrap samples of size m where m → ∞ and m/n→ 0. The choice of m is an important matter, in general. In this paper we consider an adaptive rule proposed by Bickel, Götze and va...

The bootstrap is a statistical technique used more and more widely in econometrics. While it is capable of yielding very reliable inference, some precautions should be taken in order to ensure this. Two “Golden Rules” are formulated that, if observed, help to obtain the best the bootstrap can offer. Bootstrapping always involves setting up a bootstrap data-generating process (DGP). The main typ...

Bayesian bootstrap was proposed by Rubin (1981) and its theoretical properties and application to survival models without covariates was studies by Lo (1993) and others. Bayesian bootstrap, empirical likelihood and bootstrap are diierent approaches based on the same idea, approximating the nonparametric model with the family of distributions whose supports are the set of observations. Based on ...

The cluster bootstrap resamples clusters or subjects instead of individual observations in order to preserve the dependence within each cluster or subject. In this paper, we provide a theoretical justification of using the cluster bootstrap for the inferences of the generalized estimating equations (GEE) for clustered/longitudinal data. Under the general exchangeable bootstrap weights, we show ...