ON THE RESAMPLING METHOD IN SAMPLE MEDIAN ESTIMATION

Bootstrap is one of the resampling statistical methods. This method was proposed by B. Efron. The main idea of bootstrap is to treat the original sample of values as a stand-in for the population and to resample with replacement from it repeatedly. Bootstrap allows estimation of the sampling distribution of almost any statistics using only very simple methods. This paper presents a modification of a resampling procedure based on bootstrap sampling. The proposal leads to sampling from population with density function f(x), where f(x) is estimated based on the kernel estimation. The properties of the method were analyzed in the median estimation in Monte Carlo study.The proposal could be useful for the parameters estimation in the case of a small sample. This method could be used in quality control procedures such as control charts or in the acceptance sampling

Higher-Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes

This paper investigates the accuracy of bootstrap-based inference in the case of long memory fractionally integrated processes. The re-sampling method is based on the semi-parametric sieve approach, whereby the dynamics in the process used to produce the bootstrap draws are captured by an autoregressive approximation. Application of the sieve method to data pre-filtered by a semi-parametric estimate of the long memory parameter is also explored. Higher-order improvements yielded by both forms of re-sampling are demonstrated using Edgeworth expansions for a broad class of statistics that includes first- and second-order moments, the discrete Fourier transform and regression coefficients. The methods are then applied to the problem of estimating the sampling distributions of the sample mean and of selected sample autocorrelation coefficients, in experimental settings. In the case of the sample mean, the pre-filtered version of the bootstrap is shown to avoid the distinct underestimation of the sampling variance of the mean which the raw sieve method demonstrates in finite samples, higher order accuracy of the latter notwithstanding. Pre-filtering also produces gains in terms of the accuracy with which the sampling distributions of the sample autocorrelations are reproduced, most notably in the part of the parameter space in which asymptotic normality does not obtain. Most importantly, the sieve bootstrap is shown to reproduce the (empirically infeasible) Edgeworth expansion of the sampling distribution of the autocorrelation coefficients, in the part of the parameter space in which the expansion is valid

Bootstrap Unloader-Patent

Bootstrap unloading circuits for sampling transducer voltage sources without drawing curren

Bootstrap inference for the finite population total under complex sampling designs

Bootstrap is a useful tool for making statistical inference, but it may provide erroneous results under complex survey sampling. Most studies about bootstrap-based inference are developed under simple random sampling and stratified random sampling. In this paper, we propose a unified bootstrap method applicable to some complex sampling designs, including Poisson sampling and probability-proportional-to-size sampling. Two main features of the proposed bootstrap method are that studentization is used to make inference, and the finite population is bootstrapped based on a multinomial distribution by incorporating the sampling information. We show that the proposed bootstrap method is second-order accurate using the Edgeworth expansion. Two simulation studies are conducted to compare the proposed bootstrap method with the Wald-type method, which is widely used in survey sampling. Results show that the proposed bootstrap method is better in terms of coverage rate especially when sample size is limited

Bootstrap Tests: How Many Bootstraps?

This paper discusses how to choose the number of bootstrap samples when performing bootstrap tests. There are two important issues that arise when the number of bootstraps is finite. One is bias in the estimation of bootstrap $P$ values or critical values, and the second is loss of power. We discuss an easy way to avoid bias and thus obtain exact tests if the underlying test statistic is pivotal. We also propose a simple pretest procedure for choosing the number of bootstrap samples so as to avoid power loss, and we illustrate its performance using sampling experiments.Bootstrap testing, Bootstrap samples