A canonical process for estimation of convex functions:: The invelope of integrated Brownian motion plus t4
成果类型：
Article
署名作者：
Groeneboom, P; Jongbloed, G; Wellner, JA
署名单位：
Delft University of Technology; Vrije Universiteit Amsterdam; University of Washington; University of Washington Seattle
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
2001
页码：
1620-1652
关键词：
摘要：
A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively, We call this process the invelope and show that it is an almost surely uniquely defined function of integrated Brownian motion, Its role is comparable to the role of the greatest convex minorant of Brownian motion plus a parabolic drift in the problem of estimating monotone functions. An iterative cubic spline algorithm is introduced that solves the constrained least squares problem in the limit situation and some results, obtained by applying this algorithm, are shown to illustrate the theory.