Annals of Statistics

Martingale Expansions and Second Order Inference

Per Aslak Mykland

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The paper develops a one-step triangular array Edgeworth expansion for multivariate martingales that are, essentially, asymptotically ergodic. Both discrete and continuous time are covered. The expansion is in a test function topology. We investigate when the expansion has the usual Edgeworth form, looking in particular at likelihood inference, including Cox regression, and at inference for stationary time series. The triangular array nature of the results make them useful for bootstrapping, and a result pointing in that direction is shown for Cox regression.

Article information

Ann. Statist., Volume 23, Number 3 (1995), 707-731.

First available in Project Euclid: 11 April 2007

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Zentralblatt MATH identifier


Primary: 60F99: None of the above, but in this section
Secondary: 60G42: Martingales with discrete parameter 60G44: Martingales with continuous parameter 60G55: Point processes 60J05: Discrete-time Markov processes on general state spaces 62E20: Asymptotic distribution theory 62F12: Asymptotic properties of estimators 62M09: Non-Markovian processes: estimation 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Bootstrapping Edgeworth expansions likelihood inference Markov processes martingales Cox regression time series


Mykland, Per Aslak. Martingale Expansions and Second Order Inference. Ann. Statist. 23 (1995), no. 3, 707--731. doi:10.1214/aos/1176324617.

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