Nonparametric kernel estimation for error density

Abstract

Summary form only given. Consider a linear model, y/sub i/=x'/sub i//spl beta/+e/sub i/, i=1,2,..., x'/sub i/s are p(/spl ges/1) dimension known vectors and /spl beta/(/spl isin/R/spl deg/) is an unknown parametric vector and e/sub i/ are assumed i.i.d.r.v.'s from a common unknown density function f(x) with med (e/sub i/)=0. Based on LAD (least absolute deviations) estimator /spl beta//spl tilde/ of /spl beta/, we propose a nonparametric method to estimate unknown f(x). A kernel estimator f/spl tilde//sub n/(x) is obtained. Large sample properties of f/spl tilde//sub n/(x) are studied. Some computational examples are also given.