In this paper, we propose a Bayesian semiparametric mean-covariance regression model with known covariance structures. A mixture model is used to describe the potential non-normal distribution of the regression errors. Moreover, an empirical likelihood adjusted mixture of Dirichlet process model is constructed to produce distributions with given mean and variance constraints. We illustrate through simulation studies that the proposed method provides better estimations in some non-normal cases. We also demonstrate the implementation of our method by analyzing the data set from a sleep deprivation study.
Han Jun YUJun Shan SHENZhao Nan LIXiang Zhong FANG
In lifetime data analysis, naturally recorded observations are length-biased data if the probability to select an item is proportional to its length. Based on i.i.d, observations of the true distribution, empirical likelihood （EL） procedure is proposed for the inference on mean residual life （MRL） of naturally recorded item. The limit distribution of the EL based log-likelihood ratio is proved to be the chi-square distribution. Under right censorship, since the EL based log-likelihood ratio leads to a scaled chi-square distribution and estimating the scale parameter leads to lower coverage of confidence interval, we propose an algorithm to calculate the likelihood ratio （LR） directly. The corresponding log-likelihood ratio converges to the standard chi-square distribution and the corresponding confidence interval has a better coverage. Simulation studies are used to support the theoretical results.
The maximum entropy method has been widely used in many fields, such as statistical mechanics,economics, etc. Its crucial idea is that when we make inference based on partial information, we must use the distribution with maximum entropy subject to whatever is known. In this paper, we investigate the empirical entropy method for right censored data and use simulation to compare the empirical entropy method with the empirical likelihood method. Simulations indicate that the empirical entropy method gives better coverage probability than that of the empirical likelihood method for contaminated and censored lifetime data.
