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Title: Automatic shape-constrained nonparametric regression Authors:  Huixia Wang - The George Washington University (United States) [presenting]
Yanlin Tang - George Washington University (United States)
Zhikun Gao - George Washington University (United States)
Abstract: The vocalizations of mice consist of syllables of different types determined by the frequency modulations and structure variations. To characterize the impact of social environments and genotypes on vocalizations, it is important to identify the shapes of frequency contours of syllables. Using hypothesis testing methods to determine the shapes would require testing various null and alternative hypotheses for each curve, and is impractical for vocalization studies with a large number of frequency contours. 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. Simulation shows the proposed method gives more stable curve estimation than the unconstrained B-spline estimator, and it is competitive to the shape-constrained estimator assuming prior knowledge of the functional shape. The proposed method is applied to the motivating vocalization study to examine the effect of Mecp2 gene on the vocalizations of mice during courtship.