| Inference using Shape-Restricted Regression Splines
University of Georgia
Wednesday, September 20, 2006
3:10 p.m.-4:00 p.m.
Nonparametric function estimation is appropriate when a parametric form is unknown. In practice, researchers prefer to use parametric models, because parameters are interpretable and useful inference procedures are available in statistical software packages. However, often the only valid assumptions are qualitative in nature: the expected value of the response must be increasing with the predictor variable; the growth curve must be increasing and concave; the time series trend must be decreasing. Perhaps the function can also be assumed to be smooth.
Hypothesis testing procedures where the null hypothesis is the convenient parametric form and the alternative hypothesis encompasses only the known qualtitative assumptions are therefore useful in practice. In this talk several methods are presented in which the alternative hypothesis involves assumptions about shape and smoothness. Shape-restricted regression splines are used for the fits to the data because unlike the unrestricted versions, they are robust to knot choices. Exact tests for constant versus increasing and linear versus convex regression functions are presented, as well as a practical test for linear versus increasing regression function. The methods are applied to several real-world datasets.