Estimation of the Mean of a Wiener Sheet

Abstract

A shifted Wiener sheet is observed above a decreasing curve � . By the help of a direct discrete approach and under weaker assumptions than in the paper of Arato( Comput. Math. Appl. 33 (1997), 13-25), an explicit formula is derived for the maximum likelihood estimator of the shift parameter. This estimator is a weighted linear combination of the values at the endpoints of the curve � and weighted integrals of the observed process and its normal derivative along the curve � .