Bayesian Semiparametric Methods to Test Shapes of Regression Functions

• Activity Number: 352
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yifang Li*+ and Sujit Kumar Ghosh
• Companies: North Carolina State University and North Carolina State University
• Keywords: Bayesian semiparametric method ; Bernstein polynomials ; shape restriction test ; regression ; monotonicity ; convexity

Abstract

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.