Efficient estimators for functionals of Markov chains with parametric marginals

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Abstract
Suppose we observe a geometrically ergodic Markov chain with a parametric model for the marginal, but no (further) information about the transition distribution. Then the empirical estimator for a linear functional of the joint law of two successive observations is no longer efficient. We construct an improved estimator and show that it is efficient. The construction is similar to a recent one for bivariate models with parametric marginals. The result applies to discretely observed parametric continuous-time processes.
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Author(s)
Wefelmeyer, Wolfgang
Penev, Spiridon
Peng, Hanxiang
Schick, Anton
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Publication Year
2004
Resource Type
Journal Article
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UNSW Faculty