A0561
Title: Nonparametric statistical inference for case one interval censored data
Authors: Meiling Hao - The Hong Kong Polytechnic University (Hong Kong)
Xingqiu Zhao - The Hong Kong Polytechnic University (Hong Kong)
Yuanyuan Lin - The Chinese University of Hong Kong (Hong Kong)
Kin Yat Liu - The Hong Kong Polytechnic University (Hong Kong) [presenting]
Abstract: Nonparametric maximum likelihood has been derived for the survival functions with current status data. The nonparametric maximum likelihood estimators of current status data, the estimator's self-consistency property and the confidence intervals have been studied. However, as the estimator is discrete, it is not suitable to study the density and the hazard. As hazard can give more insight about the event of interest than the survival function, numerous articles have been developed based on the hazard. Similar to the case of right censored data, kernel-based approaches were given. In order to avoid selecting the sensitive bandwidth for the estimation, spline methods have also been extended to the interval censored data. Methods with the splines did not consider the asymptotic properties of the estimators. We use the penalized likelihood method to get the estimator of the cumulative hazard function. A functional Bahadur representation will be established. Based on the technical tool, we show the estimator enjoys the pointwise asymptotic normality and the global asymptotic Gaussianity. Furthermore, the likelihood ratio test is shown, which reveals some efficient properties of the test.
