Inference in nonparametric current status models with covariates

TL;DR

This paper introduces new estimators for interval censored models with covariates, providing closed-form solutions and asymptotic tests for independence, improving inference in current status models.

Contribution

It develops simple, closed-form estimators for the distribution and intensity in nonparametric current status models with covariates, including tests for independence.

Findings

Estimators are $n^{1/2}$-consistent for piece-wise constant covariates.

Proposed asymptotic $ ext{chi}^2$ tests for independence between observations.

Sample size estimators derived for the model.

Abstract

In interval censored models with current status observations, the variables are indicators of the presence of individuals on observation intervals and covariates. When several individuals share the same observation interval, a simple procedure provides new estimators for the distribution of the observation times and their intensity, in a closed form. They are $n^{1/2}$-consistent for piece-wise constant covariates. Estimators of the sample-sizes are deduced and asymptotic $\chi^2$ tests for independence of the observations on consecutive intervals and for independence between consecutive classes for the observed individuals are proposed.