Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 1, pp. 16--41

EDGEWORTH APPROXIMATION IN THE O-U PROCESS

By

YOSHIHIDE KAKIZAWA, Hokkaido University, Japan

SUMMARY. This paper shows the validity of the (arbitrary) higher order Edgeworth expansions for the distributions of the (conditional) maximum likelihood estimator and the quasi maximum likelihood estimator of the drift parameter in the Ornstein-Uhlenbeck process {Xt} observed over [0,T], where the initial value X0 is assumed to have normal distribution so that {Xt} is stationary or X0=x is a fixed value. Using the second-order Edgeworth expansions, Berry-Esseen bounds for two estimators are also derived.

AMS (1991) subject classification. Primary 62E20; secondary 62M05.

Key words and phrases. Edgeworth expansion, Berry-Esseen bound, moderate deviation, Ornstein-Uhlenbeck (O-U) diffusion process.

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