Maximum likelihood estimation for Gaussian process with nonlinear drift
Articles
Yuliya Mishura
Taras Shevchenko National University of Kyiv, Ukraine
Kostiantyn Ralchenko
Taras Shevchenko National University of Kyiv, Ukraine
Sergiy Shklyar
Taras Shevchenko National University of Kyiv, Ukraine
Published 2018-02-20
https://doi.org/10.15388/NA.2018.1.9
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Keywords

Gaussian process
discrete observations
continuous observations
maximum likelihood estimator
strong consistency

How to Cite

Mishura Y., Ralchenko K. and Shklyar S. (2018) “Maximum likelihood estimation for Gaussian process with nonlinear drift”, Nonlinear Analysis: Modelling and Control, 23(1), pp. 120-140. doi: 10.15388/NA.2018.1.9.

Abstract

We investigate the regression model Xt = θG(t) + Bt, where θ is an unknown parameter, G is a known nonrandom function, and B is a centered Gaussian process. We construct the maximum likelihood estimators of the drift parameter θ based on discrete and continuous observations of the process X and prove their strong consistency. The results obtained generalize the paper [Yu. Mishura, K. Ralchenko, S. Shklyar, Maximum likelihood drift estimation for Gaussian process with stationary increments, Austrian J. Stat., 46(3–4): 67–78, 2017] in two directions: the drift may be nonlinear, and the noise may have nonstationary increments. As an example, the model with subfractional Brownian motion is considered.

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