Brazilian Journal of Probability and Statistics

Prediction-based estimating functions: Review and new developments

Michael Sørensen

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The general theory of prediction-based estimating functions for stochastic process models is reviewed and extended. Particular attention is given to optimal estimation, asymptotic theory and Gaussian processes. Several examples of applications are presented. In particular, partial observation of a system of stochastic differential equations is discussed. This includes diffusions observed with measurement errors, integrated diffusions, stochastic volatility models, and hypoelliptic stochastic differential equations. The Pearson diffusions, for which explicit optimal prediction-based estimating functions can be found, are briefly presented.

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Braz. J. Probab. Stat. Volume 25, Number 3 (2011), 362-391.

First available in Project Euclid: 22 August 2011

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Asymptotic normality consistency diffusion with measurement errors Gaussian process integrated diffusion linear predictors non-Markovian models optimal estimating function partially observed system Pearson diffusion statistical inference for stochastic processes stochastic differential equation stochastic volatility model superposition of diffusions


Sørensen, Michael. Prediction-based estimating functions: Review and new developments. Braz. J. Probab. Stat. 25 (2011), no. 3, 362--391. doi:10.1214/11-BJPS148.

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