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Asymptotic Statistics (Hardcover, 1990 ed.)
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Asymptotic Statistics (Hardcover, 1990 ed.)
Series: Oberwolfach Seminars, 14
Expected to ship within 10 - 15 working days
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These notes are based on lectures presented during the seminar on "
Asymptotic Statistics" held at SchloB Reisensburg, Gunzburg, May
29-June 5, 1988. They consist of two parts, the theory of
asymptotic expansions in statistics and probabilistic aspects of
the asymptotic distribution theory in nonparametric statistics. Our
intention is to provide a comprehensive presentation of these two
subjects, leading from elementary facts to the advanced theory and
recent results. Prospects for further research are also included.
We would like to thank all participants for their stimulating
discussions and their interest in the subjects, which made
lecturing very pleasant. Special thanks are due H. Zimmer for her
excellent typing. We would also like to take this opportunity to to
express our thanks to the Gesellschaft fur mathematische Forschung
and to the Deutsche Mathematiker Vereinigung, especially to
Professor G. Fischer, for the opportunity to present these lectures
and to the Birkhauser Verlag for the publication of these lecture
notes. R. Bhattacharya, M. Denker Part I: Asymptotic Expansions in
Statistics Rabi Bhattacharya 11 1. CRAMER-EDGEWORTH EXPANSIONS Let
Q be a probability measure on (IRk, B"), B" denoting the Borel
sigmafield on IR". Assume that the s - th absolute moment of Q is
finite, (1.1) P. := J II x lis Q(dx) < 00, for some integer
s;::: 3, and that Q is normalized, (1.2) J x(i)Q(dx) = 0 (1 ~ i ~
k), J x(i)x(j)Q(dx) = Dij (1 ~ i,j ~ k).
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