Open Access
August 2006 A general asymptotic scheme for inference under order restrictions
D. Anevski, O. Hössjer
Ann. Statist. 34(4): 1874-1930 (August 2006). DOI: 10.1214/009053606000000443


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, 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, and 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.


Download Citation

D. Anevski. O. Hössjer. "A general asymptotic scheme for inference under order restrictions." Ann. Statist. 34 (4) 1874 - 1930, August 2006.


Published: August 2006
First available in Project Euclid: 3 November 2006

zbMATH: 1246.62019
MathSciNet: MR2283721
Digital Object Identifier: 10.1214/009053606000000443

Primary: 62E20 , 62G07
Secondary: 60G18

Keywords: convex , Density estimation , Dependence , limit distributions , monotone , regression function estimation

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 4 • August 2006
Back to Top