Parameter estimation of a shifted Wiener sheet

Abstract

An explicit form is given for the maximum likelihood estimator of a shift parameter m of a shifted Wiener sheet W(s, t)+mg(s, t), (s, t)∈ℝ₊ ², based on observations {W(s, t)+mg(s, t):(s, t)∈G}, where g:ℝ₊ ²→ℝ is a known constraint function and G has a special shape.

Keywords:

• Wiener sheet
• L ²-Riemann integrals
• L ²-processes along a curve
• Radon–Nikodym derivative

2000 Mathematics Subject Classifications :

• 60G60
• 62F12
• 62M10

Acknowledgements

The authors are indebted to the unknown referee for the useful remarks and comments.

Research has been supported by the Hungarian Scientific Research Fund under Grant No. OTKA-T079128/2009.