Seminar Vol. 200
Title: Model Checking for Parametric Single-Index Models: A Dimension Reduction Model-Adaptive Approach
Speaker: Lixing Zhu, Hong Kong Baptist University
Time: November 28th, 2019 15:00-16:15
Venue: Conference Room 106B, IESR, Zhonghui Building (College of Economics)
About the speaker:
Dr. Zhu received his undergraduate education at Anhui University in 1982, received the Master degree of Science from the University of Science and Technology of China in 1985, and obtained his doctorate from Chinese Academy of Sciences in 1990. Dr. Zhu's research interests span many areas, including high-dimensional data analysis, time series, non/semi-parametric statistics, Monte Carlo methods, empirical process theory, biostatistics and bioinformatics.
Dr. Zhu has received a wide range of support from the NSSF of China and the RGC of Hong Kong. He was a research professor at Chinese Academy of Sciences, and had taught at the University of Hong Kong (1998-2005) before joining HKBU. He has also held several visiting positions including the Cheung Kong Chair Professorship under the joint program of Chinese Ministry of Education and Li Ka Shing Foundation, Hong Kong. Other than several prizes and awards, Dr. Zhu won The State Natural Science award (Class II) and The Humboldt Research Award of Germany. Both are the prestigious national and international award. For the latter, he is the first winner, from the Mainland, Hong Kong and Taiwan, in Science, also is still the only winner from Asia in Statistics. He is a Fellow of The American Statistical Association, Institute of Mathematical Statistics and an elected member of International Statistical Institute.
Abstract:
Local smoothing testing based on multivariate nonparametric regression estimation is one of the main model checking methodologies in the literature. However, the relevant tests suffer from typical curse of dimensionality, resulting in slow convergence rates to their limits under the null hypothesis and less deviation from the null hypothesis under alternative hypotheses. This problem prevents tests from maintaining the significance level well and makes tests less sensitive to alternative hypotheses. In this paper, a model-adaption concept in lack-of-fit testing is introduced and a dimension-reduction model adaptive test procedure is proposed for parametric single-index models. The test behaves like a local smoothing test, as if the model were univariate. It is consistent against any global alternative hypothesis and can detect local alternative hypotheses distinct from the null hypothesis at a fast rate that existing local smoothing tests can achieve only when the model is univariate. Simulations are conducted to examine the performance of our methodology. An analysis of real data is shown for illustration. The method can be readily extended to global smoothing methodology and other testing problems.
