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October 2007 Transform martingale estimating functions
T. Merkouris
Ann. Statist. 35(5): 1975-2000 (October 2007). DOI: 10.1214/009053607000000299


An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function, the Laplace transform or the probability generating function. This method involves the construction of classes of transform-based martingale estimating functions that fit into the general framework of quasi-likelihood. In the parametric setting of a discrete time stochastic process, we obtain transform quasi-score functions by projecting the unavailable score function onto the special linear spaces formed by these classes. The specification of the process by any of the main integral transforms makes possible an arbitrarily close approximation of the score function in an infinite-dimensional Hilbert space by optimally combining transform martingale quasi-score functions. It also allows an extension of the domain of application of quasi-likelihood methodology to processes with infinite conditional second moment.


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T. Merkouris. "Transform martingale estimating functions." Ann. Statist. 35 (5) 1975 - 2000, October 2007.


Published: October 2007
First available in Project Euclid: 7 November 2007

zbMATH: 1126.62074
MathSciNet: MR2363960
Digital Object Identifier: 10.1214/009053607000000299

Primary: 60E10 , 60G42 , 62M99
Secondary: 62M05 , 62M09

Keywords: efficiency , Empirical transforms , martingale information , optimality , orthogonal projection , quasi-likelihood , Semimartingale

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.35 • No. 5 • October 2007
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