A NONPARAMETRIC MODE ESTIMATE UNDER DOUBLY TRUNCATED MODEL

Abstract

The phenomenon of simultaneous left and right double truncation appears in a variety of fields, sush as in medical research. The problem of estimating the mode function for this type of data has not been addressed in the statistical literature. In this paper, we propose a new kernel estimator of the mode in the framework of randomly and doubly truncated model. We establish the strong consistency with a rate for the proposed estimate, and state its asymptotic normality. A simulation study is carried out to illustrate and evaluate the finite sample behavior of the proposed estimator.