Efficient estimators for functionals of Markov chains with parametric marginals

Spiridon Penev, Hanxiang Peng, Anton Schick and Wolfgang Wefelmeyer

Statistics & Probability Letters, 2004, vol. 66, issue 3, 335-345

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.

Keywords: Least-squares; estimator; Series; estimator; Orthonormal; basis; Efficient; influence; function; Reversible; Markov; chain; Discretely; observed; diffusion; Constrained; model (search for similar items in EconPapers)
Date: 2004
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