Asymptotic expansions and bootstrapping distributions for dependent variables: A martingale approach

DOI10.1214/aos/1176348649zbMath0759.62011OpenAlexW2010937398MaRDI QIDQ1194531

Per Aslak Mykland

Publication date: 27 September 1992

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176348649

zbMATH Keywords

law of large numbersEdgeworth expansionsdependent variablesquadratic variationscontinuous martingalesasymptotically normalasymptotically ergodic differential equation modelsbootstrapping estimatorscentral limit type conditiondistributions of estimatorsone-step triangular array asymptotic expansion

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Non-Markovian processes: estimation (62M09) Markov processes: estimation; hidden Markov models (62M05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Martingales with continuous parameter (60G44) Limit theorems in probability theory (60F99)

Related Items

Partial mixing and Edgeworth expansion ⋮ Estimating jump-diffusions using closed-form likelihood expansions ⋮ Embedding and asymptotic expansions for martingales ⋮ Maximum-likelihood estimation for diffusion processes via closed-form density expansions ⋮ High order asymptotic expansion for Wiener functionals ⋮ Wiener Spiral for Volatility Modeling ⋮ High-dimensional asymptotic expansion of the null distribution for Schott’s test statistic for complete independence of normal random variables ⋮ Asymptotic expansion and estimates of Wiener functionals ⋮ Edgeworth expansion for ergodic diffusions ⋮ Small time Edgeworth-type expansions for weakly convergent nonhomogeneous Markov chains ⋮ Asymptotic expansion formulas for functionals of \(\varepsilon\)-Markov processes with a mixing property ⋮ Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos ⋮ Asymptotic expansion of Skorohod integrals ⋮ Malliavin calculus and martingale expansion ⋮ Asymptotic expansion for the quadratic variations of the solution to the heat equation with additive white noise ⋮ Sharp connections between Berry-Esseen characteristics and Edgeworth expansions for stationary processes ⋮ On the bootstrap for Moran's \(I\) test for spatial dependence ⋮ High-dimensional asymptotic expansion of the null distribution for \(L 2\) norm based MANOVA testing statistic under general distribution