58: Testing Against Parametric Regression Function using Shape-constrained Splines with AR(p) Errors

Music City Center 

Estimating a regression function using a parametric model makes it easier to describe and interpret the relationship being studied. Many practitioners prefer this approach over using a nonparametric model. Here we consider the case of a stipulated parametric function, when there are a priori assumptions about the shape and smoothness of the true regression function in the presence of AR(p) errors. For example, suppose it is known that the function must be non-decreasing; we can test the null hypothesis of linear and increasing against the alternative of smooth and increasing, using constrained splines for the the alternative fit when there exists AR(1) errors. We show that the test is consistent and that the power approaches one as the sample size increases, if the alternative is true in the presence of AR(1) errors. There are few existing methods available for comparison with our proposed test. Through simulations, we demonstrate that our test performs well, particularly when compared to the WAVK test in the funtimes R package.

Shape restrictions

Regression splines

Parametric function

Autoregressive errors

Consistent 

Section on Nonparametric Statistics