Variance estimates based on knowledge of monotonicity and concavity properties

Abstract

In problems dealing with regression functions the choice of model and estimation method is due to a priori information about the regression function. In some situations it is motivated to consider regression functions with specific non-parametric characteristics, for instance monotonicity and/or concaVity/convexity. In situations when we only have one y-observation for each Xi we propose two new variance approximation methods, one for curves that fulfil monotonicity restrictions and one for curves that fulfil concavity/ convexity restrictions.