Abstract
Large sample theory and various estimation methods for stochastic processes are reviewed in a unified framework via martingale estimating functions. Results on asymptotic op¬timality of the estimates are discussed for both ergodic and non-ergodic processes. To illustrate the main results, various parameter estimates for GARCH-type processes, bifur¬cating and explosive autoregressive processes, conditionally linear autoregressive processes, and branching Markov processes are presented.
SY Hwang is currently Head of the Department and the Director of Research Institute of Natural Sciences, Sookmyung Womens University.
IV Basawa is a Prof. Emeritus in the Department of Statistics at the University of Georgia.
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Acknowledgement
We like to take this opportunity to acknowledge and celebrate Prof. Hira Koul’s outstanding achievements in fundamental research and his service to the statistical community over several decades. He has inspired numerous researchers around the world and helped generations of graduate students who themselves have become leaders in statistical research. We congratulate Hira for his life long achievements and contributions to the field of mathematical statistics. We thank the reviewer for careful reading of the paper. This work was supported by a grant from the National Research Foundation of Korea (NRF-2012012872).
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Hwang, S., Basawa, I. (2014). Martingale Estimating Functions for Stochastic Processes: A Review Toward a Unifying Tool. In: Lahiri, S., Schick, A., SenGupta, A., Sriram, T. (eds) Contemporary Developments in Statistical Theory. Springer Proceedings in Mathematics & Statistics, vol 68. Springer, Cham. https://doi.org/10.1007/978-3-319-02651-0_2
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