A general asymptotic scheme for inference under order restrictions

Dragi Anevski and Ola Hössjer

Abstract:: Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, both for independent, weakly dependent and long range dependent data. The results are applied to isotonic regression, isotonic regression after kernel smoothing, estimation of convex regression functions, estimation of monotone and convex density functions. Various pointwise limit distributions are obtained, and the rate of convergence depends on the self similarity; properties and on the rate of convergence of the processes considered.

Key words:: Density estimation; regression; monotonicity; convexity; deconvolution; kernel smoothing; NPMLE; long range dependence; mixing; greatest convex minorant; limit distribution.