Statistics Colloquium : Dr. Judy Wang
George Washington Univ / NSF
Friday, May 3, 2019 · 11 AM - 12 PM
Title: Automatic Shape-constrained Nonparametric Regression
Abstract : Shape information such as monotonicity and convexity of regression functions, if available, can be incorporated in nonparametric regression to improve estimation accuracy. However, in practice, the functional shapes are not always known in advance. On the other hand, using hypothesis testing to determine shapes would require testing various null and alternative hypotheses, and thus is not practical when interests are on many functional curves. To overcome this challenge, we propose a new penalization-based method, which provides function estimation and automatic shape identification simultaneously. The method estimates the functional curve through quadratic B-spline approximation, and captures the shape feature by penalizing the positive and negative parts of the first two derivatives of the spline function in a group manner. Under some regularity conditions, we show that the proposed method can identify the correct shape with probability approaching one, and the resulting nonparametric estimator can achieve the optimal convergence rate. The value of the proposed method is demonstrated through simulation and the analysis of a motivating vocalization data to examine the effect of Mecp2 gene on the vocalizations of mice during courtship.
