科学研究

Dr. YU, Tao received his B.S. degree and M.S. in Mathematics and Probability & Statistics from Nankai University in 2001 and 2004 respectively. He obtained his Ph.D. degree from University of Wisconsin-Madison in 2009. He is now associate professor in Department of Statistics and Data Science at National University of Singapore (NUS). His research interests include brain imaging data, semi- and non-parametric likelihood methods, shape constrained inference, and the high throughput gene data analysis.

The Box--Cox transformation model has been widely applied for many years. The parametric version of this model assumes that the random error follows a parametric distribution, say the normal distribution, and estimates the model parameters using the maximum likelihood method.  The semiparametric version assumes that the distribution of the random error is completely unknown; existing methods either need strong assumptions, or are less effective when the distribution of the random error significantly deviates from the normal distribution. We adopt the semiparametric assumption and propose a maximum profile binomial likelihood method. We theoretically establish the joint distribution of the estimators of the model parameters. Through extensive numerical studies, we demonstrate that our method has an advantage over existing methods when the distribution of the random error deviates from the normal distribution. Furthermore, we compare the performance of our method and existing methods on an HIV data set.