The Annals of Statistics

A general asymptotic scheme for inference under order restrictions

D. Anevski and O. Hössjer

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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

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

First available in Project Euclid: 3 November 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Limit distributions density estimation regression function estimation dependence monotone convex


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.

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