Penalized quasi likelihood estimation for variable selection

TL;DR

This paper develops a penalized quasi likelihood estimation method for stochastic differential equation models, ensuring model selection consistency through polynomial large deviation inequalities.

Contribution

It introduces a novel approach that maintains large deviation properties under penalization, aiding reliable variable selection in stochastic models.

Findings

Establishes polynomial large deviation inequality for penalized quasi likelihood

Ensures convergence of moments of the estimator

Provides bounds for incorrect model selection probability

Abstract

Penalized methods are applied to quasi likelihood analysis for stochastic differential equation models. In this paper, we treat the quasi likelihood function and the associated statistical random field for which a polynomial type large deviation inequality holds. Then penalty terms do not disturb a polynomial type large deviation inequality. This property ensures the convergence of moments of the associated estimator which plays an important role to evaluate the upper bound of the probability that model selection is incorrect.