Environmetrics

this article. 4. BOOTSTRAP SIMULATION METHOD 4.1. General Consider that a random sample of observation, X 1 ; X 2 ; ...; X n is used to obtain a sample estimate # s of a parameter of interest #, which can be a quantile or some other statistic. The purpose of bootstrap simulations is to estimate the uncertainty (bias and variance) associated with the sample estimate # s . In the standard version of bootstrap (Efron and Tibshirani, 1993), a random sample of size n is drawn with replacement from the ordered sample 1:n ; X 2:n ; ...; X n:n g as X # j F #1 E pX np#1 for j 1; n 15 where F #1 E p denotes the empirical (sample) quantile function, p is a uniform rv (0--1) and [np] denotes the integer floor function. This method is also known as non-parametric bootstrap, as no parametric DF is used for simulating bootstrap sample