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Activity Number: 353 - Contributed Poster Presentations: Section on Nonparametric Statistics
Type: Contributed
Date/Time: Tuesday, August 1, 2017 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #323295
Title: Local Signal Detection on Irregular Domains via Bivariate Splines
Author(s): Miao Yang* and Lan Xue and Lijian Yang
Companies: and Oregon State University and Tsinghua University
Keywords: local signal detection ; irregular domain ; bivariate spline ; triangulation ; penalization

Local signal detection is useful in many scientific areas such as imaging processing and speech recognition for extracting useful patterns from noisy signals. In this paper, we study estimation and local signal detection for spatial data distributed over irregular domains. We use bivariate splines defined on triangulations to approximate unknown signals on a complex domain nonparametrically. We propose a penalized polynomial spline method that simultaneously detects the null region with no signals and estimate the patter on non-zero regions. A smoothing proximal gradient (SPG) algorithm is used to find the estimator efficiently. In theory, the proposed estimator is shown to be consistent in estimating the underling true signals. In addition, it is also able to detect the null signal region with probability with probability approaching to one. The numeric performances of the proposed method is evaluated by simulation studies and real data analysis. It shows that the proposed method and algorithm efficiently detect local signals on complex domains.

Authors who are presenting talks have a * after their name.

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