Journal
SANKHYA-SERIES A-MATHEMATICAL STATISTICS AND PROBABILITY
Volume 79, Issue 2, Pages 215-253Publisher
SPRINGER
DOI: 10.1007/s13171-017-0104-8
Keywords
Convex function estimation; Integral of Brownian motion; Invelope process; Least squares estimator; Shape constrained regression
Categories
Funding
- NSF [DMS-1150435]
Ask authors/readers for more resources
We find the local rate of convergence of the least squares estimator (LSE) of a one dimensional convex regression function when (a) a certain number of derivatives vanish at the point of interest, and (b) the true regression function is locally affine. In each case we derive the limiting distribution of the LSE and its derivative. The pointwise limiting distributions depend on the second and third derivatives at 0 of the invelope function of the integral of a two-sided Brownian motion with polynomial drifts. We also investigate the inconsistency of the LSE and the unboundedness of its derivative at the boundary of the domain of the covariate space. An estimator of the argmin of the convex regression function is proposed and its asymptotic distribution is derived. Further, we present some new results on the characterization of the convex LSE that may be of independent interest.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available