The Bootstrap method application in simulation supposes that value of random variables are not generated during the simulation process but extracted from available sample populations. In the case of Hierarchical Bootstrap the function of interest is calculated recurrently using the calculation tree. In the present paper we consider the optimization of sample sizes in each vertex of the calculat...

In this paper a new block bootstrap method for periodic times series called Generalized Seasonal Tapered Block Bootstrap (GSTBB) is introduced. Consistency of the GSTBB for parameters associated with periodically correlated time series is shown; these are the overall mean, seasonal means and Fourier coefficients of the autocovariance function. Consequently, the construction of bootstrap pointwi...

The construction of the simultaneous confidence bands for the integrated hazard function is considered. The Nelson–Aalen estimator is used. The simultaneous confidence bands based on bootstrap methods are presented. Two methods of construction of such confidence bands are proposed. The weird bootstrap method is used for resampling. Simulations are made to compare the actual coverage probability...

This paper contains supplemental materials for Marmer, Shneyerov, and Xu (2011), MSX hereafter. It establishes validity of the bootstrap delta-method expansion (65) in Appendix E of MSX. In what follows, the statistics with superscript † denote the bootstrap analogues of the statistics computed using the original data. To simplify the notion, we will suppress the subscript indicating the bootst...

A new bootstrap procedure for unit root testing based on the tapered block bootstrap is introduced. This procedure is similar to previous tests that were based on the block bootstrap and stationary bootstrap, but it has the advantage of the tapering procedure that has been previously shown to reduce the bias of the variance estimator by an order of magnitude. In this paper, the procedure is def...

While the bootstrap in its first two decades after its inception by Brad Efron revolutionized the methods of the expert data analysts, its vast pedagogical potential is still in the process of being discovered. The bootstrap is a prime example of synergy between technology and content that can naturally be taught within the paradigms of new pedagogy. It has the potential to make core concepts o...

Bootstrap tilting con dence intervals could be the method of choice in many applications for reasons of both speed and accuracy With the right implementa tion tilting intervals are times as fast as bootstrap BC a limits in terms of the number of bootstrap sam ples needed for comparable simulation accuracy Thus bootstrap samples might su ce instead of Tilting limits have other desirable properti...

Because the stationary bootstrap resamples data blocks of random length, this method has been thought to have the largest asymptotic variance among block bootstraps (Lahiri, 1999, Ann. Statist.). It is shown here that the variance of the stationary bootstrap surprisingly matches that of a block bootstrap based on non-random, non-overlapping blocks. This argument translates the variance expansio...

We study a bootstrap method for stationary real-valued time series, which is based on the method of sieves. We restrict ourselves to autoregressive sieve bootstraps. Given a sample X1; : : : ; Xn from a linear process fXtgt2ZZ, we approximate the underlying process by an autoregressive model with order p = p(n), where p(n)!1; p(n) = o(n) as the sample size n!1. Based on such a model a bootstrap...

Gini coefficient is among the most popular and widely used measures of income inequality in economic studies, with various extensions and applications in finance and other related areas. This paper studies confidence intervals on the Gini coefficient for simple random samples, using normal approximation, bootstrap percentile, bootstrap-t and the empirical likelihood method. Through both theory ...