Testing the monotonicity or convexity of a function using regression splines (2010)

Abstract:

Methods for smoothed isotonic or convex regression are useful in many applications. Sometimes the shape assumptions constitute a-priori knowledge about the regression function, but often the shape is part of the research question. The authors propose tests for monotonicity and convexity using constrained and unconstrained regression splines. The tests have good large-sample properties and the small-sample behavior is illustrated through simulations. Extensions to the partial linear model and the generalized regression model are presented.

Keywords:

constrained estimation; convex; generalized regression; isotonic; monotone; partial linear model; shape restrictions.