Minimax estimation for Varying Coefficient Model via Laguerre Series

TL;DR

This paper introduces a Laguerre series-based estimator for varying coefficient models that achieves optimal convergence rates and allows for inference, demonstrated through simulations and real data analysis.

Contribution

It develops a novel Laguerre series estimator for functional coefficients in varying coefficient models with proven asymptotic optimality and inference capabilities.

Findings

Estimator attains asymptotically optimal convergence rates.

Constructs confidence intervals and hypothesis tests for coefficients.

Performs well in simulations and real data applications.

Abstract

We delve into the estimation of the functional coefficients and inference for varying coefficient model. Applying Laguerre series, we develop an estimator for the vector of functional coefficients that attains asymptotically optimal convergence rates in the minimax sense. These rates are derived for functional coefficients that belong to Laguerre-Sobolev space. The method is based on approximating the functional coefficients using truncated Laguerre series and choosing empirical Laguerre coefficients that minimize the least squares criterion. In addition, we establish the asymptotic normality of the estimator for the functional coefficients, construct their confidence intervals, and establish point-wise hypothesis tests about their true values. A simulations study is carried out to examine the finite-sample properties of the proposed methodology. A real data set is considered as well, and results based on the proposed methodology are compared to those based on selected existing approaches.