Cookies?
Library Header Image
LSE Research Online LSE Library Services

On convex least squares estimation when the truth is linear

Chen, Yining and Wellner, Jon A. (2016) On convex least squares estimation when the truth is linear. Electronic Journal of Statistics, 10 (1). pp. 171-209. ISSN 1935-7524

[img]
Preview
PDF - Published Version
Available under License Creative Commons Attribution.

Download (538kB) | Preview
Identification Number: 10.1214/15-EJS1098

Abstract

We prove that the convex least squares estimator (LSE) attains a n−1/2n−1/2 pointwise rate of convergence in any region where the truth is linear. In addition, the asymptotic distribution can be characterized by a modified invelope process. Analogous results hold when one uses the derivative of the convex LSE to perform derivative estimation. These asymptotic results facilitate a new consistent testing procedure on the linearity against a convex alternative. Moreover, we show that the convex LSE adapts to the optimal rate at the boundary points of the region where the truth is linear, up to a log-log factor. These conclusions are valid in the context of both density estimation and regression function estimation.

Item Type: Article
Official URL: http://projecteuclid.org/ejs
Additional Information: © 2016 The Authors © CC BY 2.5
Divisions: Statistics
Subjects: Q Science > QA Mathematics
Sets: Departments > Statistics
Date Deposited: 14 Mar 2016 16:54
Last Modified: 20 Oct 2019 23:14
URI: http://eprints.lse.ac.uk/id/eprint/65729

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics