ON THE RESAMPLING METHOD IN SAMPLE MEDIAN ESTIMATION

Abstract

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.

Keywords

• bootstrap, kernel estimation, small sample