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?ve expansions.

AMS Subject Classification (1991): 60G60, 62M10, 62M30

Keyword(s): Wiener sheet, Ornstein--Uhlenbeck sheet, maximum likelihood estimation, Radon--Nikodym derivative

Received April 2, 2012. (Registered under 19/2012.)