Influence curves for randomly truncated data

Abstract

Under a random truncation model, observations (X, Y) are lost if X < Y. Properties of the maximum likelihood estimators for the distributions F , G of X and Y and the truncation proportion a have been treated by various authors, for example, Lynden-Bell (1971), and more recently Woodroofe (1985). Asymptotic variances of various estimates, including the mean, the median, the L - and the M -estimates and â, if they can be expressed as functionals of ^ and Ĝ, are obtained through the concept of influence curves. The asymptotic variance of â is derived to illustrate our method.