New EM-type algorithms for the analysis of truncated normal data and its application

  • 报告人: 田国梁教授
  • 报告人单位: 南方科技大学数学系
  • 报告地址: 数学学院西303报告厅
  • 报告时间: 5月28日 9:20--10:00
  • 主题摘要:
To analyze univariate truncated normal data, in this talk, we stochastically represent the normal random variable as a mixture of a truncated normal random variable and its complementary random variable. This stochastic representation (SR) is a new idea and it is the first time to appear in literature. According to this SR, we derive important distributional properties for the truncated normal distribution and develop two new expectation--maximization (EM) algorithms to calculate the maximum likelihood estimates (MLEs) of parameters of interest for Type I data (without and with covariates) and Type II/III data. Bootstrap confidence intervals of parameters for small sample sizes are provided. To evaluate the performance of the proposed methods for the truncated normal distribution, in simulation studies, we first focus on the comparison of estimation results between including the unobserved data counts and excluding the unobserved data counts, and we next investigate the impact of the number of unobserved data on the estimation results. The plasma ferritin concentration data collected by Australian Institute of Sport and the blood fat content data are used to illustrate the proposed methods and to compare the truncated normal distribution with the half normal, the folded normal and the folded normal slash distributions based on AIC and BIC. (This is a joint work with Dr. Da JU, Prof. Kam Chuen YUEN and Miss Chi ZHANG)