Optimal Estimation for General Gaussian Processed

Tetsuya Takabatake (), Jun Yu and Chen Zhang ()
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Tetsuya Takabatake: Graduate School of Engineering Science, University of Osaka
Chen Zhang: Faculty of Business Administration, University of Macau

No 202535, Working Papers from University of Macau, Faculty of Business Administration

Abstract: This paper proposes a novel exact maximum likelihood (ML) estimation method for general Gaussian processes, where all parameters are estimated jointly. The exact ML estimator (MLE) is consistent and asymptotically normally distributed.We prove the local asymptotic normality (LAN) property of the sequence of statistical experiments for general Gaussian processes in the sense of Le Cam, thereby enabling optimal estimation and statistical inference. The results rely solely on the asymptotic behavior of the spectral density near zero, allowing them to be widely applied. The established optimality not only addresses the gap left by Adenstedt (1974), who proposed an efficient but infeasible estimator for the long-run mean µ, but also enables us to evaluate the finite-sample performance of the commonly used plug-in MLE, in which the sample mean is substituted into the likelihood. Our simulation results show that the plug-in MLE performs nearly as well as the exact MLE, alleviating concerns that inefficient estimation of µ would compromise the efficiency of the remaining parameter estimates.

Keywords: General Gaussian processes; Maximum likelihood estimation; Local asymptotic normality (search for similar items in EconPapers)
Pages: 70 pages
Date: 2025-09
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Published in UM-FBA Working Paper Series

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Working Paper: Optimal Estimation for General Gaussian Processes (2025)
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