Work

On convex least squares estimation when the truth is linear

Year: 2016

Type: article

Abstract: 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.

Source: Electronic Journal of Statistics

DOI: 10.1214/15-ejs1098

Authors: Yining Chen, Jon A. Wellner

Institutions: University of Washington, London School of Economics and Political Science

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675