A general asymptotic scheme for inference under order restrictions

Details A general asymptotic scheme for inference under order restrictions A general asymptotic scheme for inference under order restrictions

2006-11-09

arxiv.org/abs/math/0611270v1

Annals of Statistics 2006, Vol. 34, No. 4, 1874-1930

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000443 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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.

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