J. Japan Statist. Soc., Vol. 33 (No. 2), pp. 145-156, 2003

Asymptotic Expansion Under Degeneracy

Yuji Sakamoto and Nakahiro Yoshida

Abstract. We will consider a stochastic expansion described by random variables whose covariance matrix is asymptotically degenerate. Though the conventional approach with Bhattacharya-Ghosh's transform requires the nondegeneracy of the covariance matrix, it is known that this method still works even in degenerate cases with the help of the so-called global approach. In this paper, we explain this fact and also mention, as an example, the third order asymptotic expansion of the maximum likelihood estimator for the O-U process.

Key words and phrases: Asymptotic expansion, diffusion functional, M-estimator, mixing process.

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