Censored Partial Linear Models and Empirical Likelihood

✍ Scribed by Gengsheng Qin; Bing-Yi Jing

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 178 KB
• Volume: 78
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.2000.1944

✦ Synopsis

Consider the partial linear model Y i =X { i ;+ g(T i )+= i , i=1, ..., n, where ; is a p_1 unknown parameter vector, g is an unknown function, X i 's are p_1 observable covariates, T i 's are other observable covariates in [0, 1], and Y i 's are the response variables. In this paper, we shall consider the problem of estimating ; and g and study their properties when the response variables Y i are subject to random censoring. First, the least square estimators for ; and kernel regression estimator for g are proposed and their asymptotic properties are investigated. Second, we shall apply the empirical likelihood method to the censored partial linear model. In particular, an empirical log-likelihood ratio for ; is proposed and shown to have a limiting distribution of a weighted sum of independent chi-square distributions, which can be used to construct an approximate confidence region for ;. Some simulation studies are conducted to compare the empirical likelihood and normal approximation-based method.