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Activity Number: 352
Type: Contributed
Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #304899
Title: Bayesian Semiparametric Methods to Test Shapes of Regression Functions
Author(s): Yifang Li*+ and Sujit Kumar Ghosh
Companies: North Carolina State University and North Carolina State University
Address: 2311 Stinson Dr., Raleigh, NC, 27695, United States
Keywords: Bayesian semiparametric method ; Bernstein polynomials ; shape restriction test ; regression ; monotonicity ; convexity

In many applied sciences, the regression function is often known to satisfy various shape constraints, such as monotonicity, convexity or both. For example, growth curves are expected to be non-decreasing and concave. However, due to the variability of the measurements, it may not be obvious to detect a specific shape of the trend using a scatter plot. This necessitates a formal statistical test to distinguish between a given class of possible shapes of a regression function (e.g., concave increasing vs. convex increasing etc.). Although various tests have been explored within frequentist framework, the testing procedures are not so easy to implement in practice. This paper develops a semiparametric Bayesian method based on a sequence of Bernstein polynomials to test a general class of shapes of regression functions. Empirical results are presented to illustrate the simplicity and efficiency of the proposed method using simulated and real data sets.

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