Non-asymptotic approach to varying coefficient model

TL;DR

This paper introduces a non-asymptotic estimation method for the varying coefficient model, providing finite-sample guarantees and bounds, addressing practical limitations of traditional asymptotic approaches.

Contribution

It proposes a novel matrix estimation-based estimator with non-asymptotic error bounds for finite samples in varying coefficient models.

Findings

Derived upper bounds for mean squared errors

Established non-asymptotic oracle inequalities

Validated effectiveness for finite sample sizes

Abstract

In the present paper we consider the varying coefficient model which represents a useful tool for exploring dynamic patterns in many applications. Existing methods typically provide asymptotic evaluation of precision of estimation procedures under the assumption that the number of observations tends to infinity. In practical applications, however, only a finite number of measurements are available. In the present paper we focus on a non-asymptotic approach to the problem. We propose a novel estimation procedure which is based on recent developments in matrix estimation. In particular, for our estimator, we obtain upper bounds for the mean squared and the pointwise estimation errors. The obtained oracle inequalities are non-asymptotic and hold for finite sample size.