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Optimal estimation for semimartingales

Published online by Cambridge University Press:  14 July 2016

A. Thavaneswaran  and
M. E. Thompson
A. Thavaneswaran*
Affiliation:
University of Waterloo
M. E. Thompson*
Affiliation:
University of Waterloo
*
∗ Postal address: Department of Statistics and Actuarial Science, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
∗ Postal address: Department of Statistics and Actuarial Science, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
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Abstract

This paper extends a result of Godambe's theory of parametric estimation for discrete-time stochastic processes to the continuous-time case. Let P ={P} be a family of probability measures such that (Ω, F, P) is complete, (Ft, t≧0) is a standard filtration, and X = (Xt Ft, t ≧ 0) is a semimartingale for every P ∈ P. For a parameter θ (Ρ), suppose Xt = Vt ,θ + Ht,θ where the Vθ process is predictable and locally of bounded variation and the Hθ process is a local martingale. Consider estimating equations for θ of the form process is predictable. Under regularity conditions, an optimal form for α θ in the sense of Godambe (1960) is determined. When Vt,θ is linear in θ the optimal , corresponds to certain maximum likelihood or least squares estimates derived previously in special cases. Asymptotic properties of , are discussed.

Keywords

ESTIMATING FUNCTIONS: STOCHASTIC INTEGRALS

Information

Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 409 - 417
Copyright
Copyright © Applied Probability Trust 1986 

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