Resampling: Theory and Applications

Abstract

Let X = (X1,..., Xn) be the random sample obtained from some unknown distribution F. Let \theta = T(F) be the parameter of interest estimated by \hat\theta = S(X). We discuss bias and variance estimators for \hat\theta obtained by resampling methods such as jackknife and bootstrap. Along these lines, we try to extrapolate these methods originally introduced for independent data set to specific models such as linear model and Dependent data set. More specifically, we consider least square estimates for the linear model and apply resampling methods for the bias and the variance estimates for the same. Time series model has been looked at in dependent data sequence and these resampling procedures have been modified to produce a consistent estimates for the statistic of interest