Information bounds for Gaussian copula parameter in stationary semiparametric Markov models

Xiaohong Chen and Yanping Yi

Statistics & Probability Letters, 2025, vol. 216, issue C

Abstract: Let {Vt}t=1n be any univariate stationary first-order semiparametric Markov process generated from an unknown invariant marginal distribution and a bivariate Gaussian copula with unknown correlation coefficient α0∈(−1,1). We prove that 1−α02 is the semiparametric efficient variance bound for estimating the correlation parameter α0 in any Gaussian copula generated first-order stationary Markov models. Surprisingly, this variance bound is strictly larger than 1−α022 (when α0≠0), which is the semiparametric efficient variance bound derived by Klaassen and Wellner (1997) for estimating the correlation parameter using any i.i.d. data {(Xi,Yi)}i=1n generated from a bivariate Gaussian copula with two unknown marginal distributions.

Keywords: Gaussian copula; First-order Markov models; Semiparametric Fisher information bound (search for similar items in EconPapers)
JEL-codes: C14 C22 G32 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2024.110254

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