Parameter estimation in linear regression driven by a Gaussian sheet

Sándor Baran; Kinga Sikolya

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arXiv · 1111.2205

Parameter estimation in linear regression driven by a Gaussian sheet

Sándor Baran·Kinga Sikolya

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Abstract

The problem of estimating the parameters of a linear regression model $Z(s,t)=m_1g_1(s,t)+ \cdots + m_pg_p(s,t)+U(s,t)$ based on observations of $Z$ on a spatial domain $G$ of special shape is considered, where the driving process $U$ is a Gaussian random field and $g_1, \ldots, g_p$ are known functions. Explicit forms of the maximum likelihood estimators of the parameters are derived in the cases when $U$ is either a Wiener or a stationary or nonstationary Ornstein-Uhlenbeck sheet. Simulation results are also presented, where the driving random sheets are simulated with the help of their Karhunen-Lo\`eve expansions.

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Sándor Baran, Kinga Sikolya. 2011-11-09. Parameter estimation in linear regression driven by a Gaussian sheet. https://arxiv.org/abs/1111.2205

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