A new kernel estimator of hazard ratio and its asymptotic mean squared error
Abstract
The hazard function is a ratio of a density and survival function, and it is a basic tool of the survival analysis. In this paper we propose a kernel estimator of the hazard ratio function, which are based on a modification of \'Cwik and Mielniczuk's method. We study nonparametric estimators of the hazard function and compare those estimators by means of asymptotic mean squared error (AMSE). We obtain asymptotic bias and variance of the new estimator, and compare them with a naive estimator. The asymptotic variance of the new estimator is always smaller than the naive estimator's, so we also discuss an improvement of AMSE using Terrell and Scott's bias reduction method. The new modified estimator ensures the non-negativity, and we demonstrate the numerical improvement.