  Given noisy data, function estimation is considered when the unknown function
is known apriori to consist of a small number of regions where the function is
either convex or concave. When the regions are known apriori, the estimate is
reduced to a finite dimensional convex optimization in the dual space. When the
number of regions is unknown, the model selection problem is to determine the
number of convexity change points. We use a pilot estimator based on the
expected number of false inflection points.
