Resampling

About: Resampling is a research topic. Over the lifetime, 5428 publications have been published within this topic receiving 242291 citations.

On bootstrap resampling and iteration

Abstract: SUMMARY We propose a single unifying approach to bootstrap resampling, applicable to a very wide range of statistical problems. It enables attention to be focused sharply on one or more characteristics which are of major importance in any particular problem, such as coverage error or length for confidence intervals, or bias for point estimation. Our approach leads easily and directly to a very general form of bootstrap iteration, unifying and generalizing present disparate accounts of this subject. It also provides simple solutions to relatively complex problems, such as a suggestion by Lehmann (1986) for 'conditionally' short confidence intervals. We set out a single unifying principle guiding the operation of bootstrap resampling, applicable to a very wide range of statistical problems including bias reduction, shrinkage, hypothesis testing and confidence interval construction. Our principle differs from other approaches in that it focuses attention directly on a measure of quality or accuracy, expressed in the form of an equation whose solution is sought. A very general form of bootstrap iteration is an immediate consequence of iterating the empirical solution to this equation so as to improve accuracy. When employed for bias reduction, iteration of the resampling principle yields a competitor to the generalized jackknife, enabling bias to be reduced to arbitrarily low levels. When applied to confidence intervals it produces the techniques of Hall (1986) and Beran (1987). The resampling principle leads easily to solutions of new, complex problems, such as empirical versions of confidence intervals proposed by Lehmann (1986). Lehmann argued that an 'ideal' confidence interval is one which is short when it covers the true parameter value but not necessarily otherwise. The resampling principle suggests a simple empirical means of constructing such intervals. Section 2 describes the general principle, and ? 3 shows how it leads naturally to bootstrap iteration. There we show that in many problems of practical interest, such as bias reduction and coverage-error reduction in two-sided confidence intervals, each iteration reduces error by the factor n-1, where n is sample size. In the case of confidence intervals our result sharpens one of Beran (1987), who showed that coverage error is reduced by the factor n-2 in two-sided intervals. The main exception to our n-1 rule is coverage error of one-sided intervals, where error is reduced by the factor n-A at each iteration. Our approach to bootstrap iteration serves to unify not just the philosophy of iteration for different statistical problems, but also different techniques of iteration for the same

Hiding Traces of Resampling in Digital Images

Abstract: Resampling detection has become a standard tool for forensic analyses of digital images. This paper presents new variants of image transformation operations which are undetectable by resampling detectors based on periodic variations in the residual signal of local linear predictors in the spatial domain. The effectiveness of the proposed method is supported with evidence from experiments on a large image database for various parameter settings. We benchmark detectability as well as the resulting image quality against conventional linear and bicubic interpolation and interpolation with a sinc kernel. These early findings on ldquocounter-forensicrdquo techniques put into question the reliability of known forensic tools against smart counterfeiters in general, and might serve as benchmarks and motivation for the development of much improved forensic techniques.

The use of bootstrapping when using propensity-score matching without replacement: a simulation study

Abstract: Propensity-score matching is frequently used to estimate the effect of treatments, exposures, and interventions when using observational data. An important issue when using propensity-score matching is how to estimate the standard error of the estimated treatment effect. Accurate variance estimation permits construction of confidence intervals that have the advertised coverage rates and tests of statistical significance that have the correct type I error rates. There is disagreement in the literature as to how standard errors should be estimated. The bootstrap is a commonly used resampling method that permits estimation of the sampling variability of estimated parameters. Bootstrap methods are rarely used in conjunction with propensity-score matching. We propose two different bootstrap methods for use when using propensity-score matching without replacementand examined their performance with a series of Monte Carlo simulations. The first method involved drawing bootstrap samples from the matched pairs in the propensity-score-matched sample. The second method involved drawing bootstrap samples from the original sample and estimating the propensity score separately in each bootstrap sample and creating a matched sample within each of these bootstrap samples. The former approach was found to result in estimates of the standard error that were closer to the empirical standard deviation of the sampling distribution of estimated effects.

A General Resampling Scheme for Triangular Arrays of $\alpha$-Mixing Random Variables with Application to the Problem of Spectral Density Estimation

Abstract: In 1989 Kunsch introduced a modified bootstrap and jackknife for a statistic which is used to estimate a parameter of the $m$-dimensional joint distribution of stationary and $\alpha$-mixing observations. The modification amounts to resampling whole blocks of consecutive observations, or deleting whole blocks one at a time. Liu and Singh independently proposed (in 1988) the same technique for observations that are $m$-dependent. However, many time-series statistics, notably estimators of the spectral density function, involve parameters of the whole (infinite-dimensional) joint distribution and, hence, do not fit in this framework. In this report we generalize the "moving blocks" resampling scheme of Kunsch and Liu and Singh; a still modified version of the nonparametric bootstrap and jackknife is seen to be valid for general linear statistics that are asymptotically normal and consistent for a parameter of the whole joint distribution. We then apply this result to the problem of estimation of the spectral density.

Resampling methods for evaluating classification accuracy of wildlife habitat models

Abstract: Predictive models of wildlife-habitat relationships often have been developed without being tested The apparent classification accuracy of such models can be optimistically biased and misleading. Data resampling methods exist that yield a more realistic estimate of model classification accuracy These methods are simple and require no new sample data. We illustrate these methods (cross-validation, jackknife resampling, and bootstrap resampling) with computer simulation to demonstrate the increase in precision of the estimate. The bootstrap method is then applied to field data as a technique for model comparison We recommend that biologists use some resampling procedure to evaluate wildlife habitat models prior to field evaluation.