Abstract:
We study the problem of nonparamateric estimation of the conditional distribution function when we have current status data on the outcome variable and a single continuous-valued covariate. An estimator of the conditional distribution function F(Y|X = x), called the local nonparametric maximum likelihood estimator (LNPMLE) is proposed. This estimator is a locally weighted version of the nonparametric maximum likelihood estimator (NPMLE) for current status data in the absence of covariates. The primary goal of this work is to obtain an expression for the optimal bandwidth used to pick neighborhood size. The asymptotic distribution for the LNPMLE of the conditional distribution function at a point, F(t|X = x), is studied, and the asymptotically optimal bandwidth is shown to be of the order n-1/7. The LNPMLE of the conditional distribution function can be obtained as a solution to a weighted isotonic regression problem. A plug-in estimate is suggested for the bandwidth, and the computation of the LNPMLE is illustrated on a simulated sample.
tr127.pdf