Mixed domain asymptotics for a stochastic process model with time trend and measurement error

TL;DR

This paper analyzes the asymptotic behavior of maximum likelihood estimators for a stochastic process model with a time trend and measurement error, covering various domain growth scenarios and model complexities.

Contribution

It establishes consistency and limiting distributions of ML estimators under a unified framework including fixed and increasing domain asymptotics, even with model misspecification.

Findings

Convergence rates depend on domain growth and model complexity.

ML estimators are consistent under general conditions.

Limiting distributions are derived for various asymptotic regimes.

Abstract

We consider a stochastic process model with time trend and measurement error. We establish consistency and derive the limiting distributions of the maximum likelihood (ML) estimators of the covariance function parameters under a general asymptotic framework, including both the fixed domain and the increasing domain frameworks, even when the time trend model is misspecified or its complexity increases with the sample size. In particular, the convergence rates of the ML estimators are thoroughly characterized in terms of the growing rate of the domain and the degree of model misspecification/complexity.