The Annals of Statistics

A general asymptotic scheme for inference under order restrictions

D. Anevski and O. Hössjer

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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, 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.

Article information

Source
Ann. Statist., Volume 34, Number 4 (2006), 1874-1930.

Dates
First available in Project Euclid: 3 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1162567637

Digital Object Identifier
doi:10.1214/009053606000000443

Mathematical Reviews number (MathSciNet)
MR2283721

Zentralblatt MATH identifier
1246.62019

Subjects
Primary: 62E20: Asymptotic distribution theory 62G07: Density estimation
Secondary: 60G18: Self-similar processes

Keywords
Limit distributions density estimation regression function estimation dependence monotone convex

Citation

Anevski, D.; Hössjer, O. A general asymptotic scheme for inference under order restrictions. Ann. Statist. 34 (2006), no. 4, 1874--1930. doi:10.1214/009053606000000443. https://projecteuclid.org/euclid.aos/1162567637


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