Target estimation for bias and mean square error reduction

Abstract

Given a statistical functional T and a parametric family of distributions, a bias reduced functional $\tilde{T}$ is defined by setting the expected value of the statistic equal to the observed value. Under certain regularity conditions this new statistic, called the target estimator, will have smaller bias and mean square error than the original estimator. The theoretical aspects are analyzed by using higher order von Mises expansions. Several examples are given, including $M$-estimates of location and scale. The procedure is applied to an autoregressive model, the errors-in-variables model and the logistic regression model. A comparison with the jackknife and the bootstrap estimators is also included.