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A general asymptotic scheme for inference under order restrictions. (English) Zbl 1246.62019

Summary: 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.

MSC:

62E20 Asymptotic distribution theory in statistics
62M99 Inference from stochastic processes
62G08 Nonparametric regression and quantile regression
62F30 Parametric inference under constraints
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