Partial quasi likelihood analysis

TL;DR

This paper extends quasi likelihood analysis to a partial setting, deriving limit theorems for estimators under slow mixing conditions where traditional inequalities do not apply, with illustrative examples.

Contribution

It introduces partial quasi likelihood analysis and establishes new limit theorems for estimators in complex mixing scenarios.

Findings

Derived limit theorems for quasi likelihood estimators.

Established results for quasi Bayesian estimators under slow mixing.

Provided illustrative examples demonstrating the theory.

Abstract

The quasi likelihood analysis is generalized to the partial quasi likelihood analysis. Limit theorems for the quasi likelihood estimators, especially the quasi Bayesian estimator, are derived in the situation where existence of a slow mixing component prohibits the Rosenthal type inequality from applying to the derivation of the polynomial type large deviation inequality for the statistical random field. We give two illustrative examples.