A Test for Constant Versus Monotone Regression Function in the Presence of Correlated Errors

• Activity Number: 504
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Huan Wang*+ and Mary C Meyer and Jean Opsomer
• Companies: and Colorado State University and Colorado State University
• Keywords: hypothesis test ; constant versus monotone ; correlated data ; shape restriction ; penalized spline

Abstract

Traditional statistical tests for the significance of a trend rely on restrictive assumptions on the shape of the relationship, e.g. linearity. In this talk, we describe a new one-sided test based on shape-restricted inference. The null hypothesis is that the underlying regression function is constant, and the alternative is that it is monotone. Also, instead of classical independent error case, the proposed test is in the situation of correlated data. This test can be widely used in exploring the effect of the potentially beneficial factors on the yield for time series data, and other analogous research areas. Robertson, Wright and Dyskstra (1988) studied the independent error case and derived the exact distribution for a likelihood ratio test statistic. We investigated the asymptotic distribution of a likelihood ratio test statistic when the correlation is unknown and the effect of the correlation on the characteristics of the test statistic. The comparison of the power of the test with the constrained penalized spline alternative and the test with the traditional linear regression alternative will be conducted.