Semiparametric maximum likelihood estimation for a two‐sample density ratio model with right‐censored data

Abstract

AbstractIn this paper we investigate a broader semiparametric two‐sample density ratio model based on two groups of right‐censored data. A semiparametric maximum likelihood estimator for the unknown finite and infinite dimensional parameters of the model is proposed and obtained by an EM algorithm. By using empirical process theory, we establish the uniform consistency and asymptotic normality of the proposed estimator. We moreover employ a Kolmogorov–Smirnov type test statistic to evaluate the model validity and a likelihood ratio test statistic to examine the treatment effects between the two groups. Simulation studies are conducted to assess the finite sample performance of the proposed estimator and to compare it with its alternatives. Finally a real data example is analyzed to illustrate its application. The Canadian Journal of Statistics 44: 58–81; 2016 © 2015 Statistical Society of Canada