Stochastic Search for Semiparametric Linear Regression Models

TL;DR

This paper presents a stochastic search approach for estimating parameters in semiparametric linear regression models, aiming to efficiently identify parameters close to the true value by exploring a random subset of the parameter space.

Contribution

It introduces a novel stochastic search method tailored for semiparametric linear regression, extending previous techniques to handle models with log-concave error distributions.

Findings

The method effectively identifies parameters near the true value.

It provides a computationally feasible approach for complex regression models.

The approach is theoretically analyzed for consistency and efficiency.

Abstract

This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar (1987). The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Duembgen, Samworth and Schuhmacher (2011) on regression models with log-concave error distributions.