A general asymptotic scheme for inference under order restrictions
Journal article, 2006
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. © Institute of Mathematical Statistics, 2006.
subordination
range dependent sequences
nonparametric regression
monotone regression
convergence
empirical process
density
estimators
sums
brownian-motion
Author
Dragi Anevski
University of Gothenburg
Chalmers, Mathematical Sciences
O. Hossjer
Lunds Universitet
Stockholms universitet
Annals of Statistics
0090-5364 (ISSN)
Vol. 34 4 1874-1930Subject Categories (SSIF 2011)
Probability Theory and Statistics
DOI
10.1214/009053606000000443