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

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.

Published at http://dx.doi.org/10.3150/15-BEJ740 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (4)

• Correction. Efficient parameter estimation for self-similar processes
• Uniform moment bounds of Fisher's information with applications to time series
• Asymptotic theory of generalized information criterion for geostatistical regression model selection
• Moment bounds and mean squared prediction errors of long-memory time series

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