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Estimation of the Mean of a Wiener Sheet


A shifted Wiener sheet is observed above a decreasing curve Γ. By the help of a direct discrete approach and under weaker assumptions than in the paper of Arató [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 Γ and weighted integrals of the observed process and its normal derivative along the curve Γ.

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Baran, S., Pap, G. & Van Zuijlen, M.C.A. Estimation of the Mean of a Wiener Sheet. Statistical Inference for Stochastic Processes 7, 279–304 (2004).

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  • maximum likelihood estimator
  • Radon-Nikodym derivatives
  • stochastic integral along a curve
  • weighted integral of the normal derivative of a random process along a curve
  • Wiener sheet