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Asymptotics in statistics: some basic concepts. (English) Zbl 0719.62003
Springer Series in Statistics. New York etc.: Springer-Verlag. viii, 180 p. DM 58.00/hbk (1990).
This book grew out of the well-known Montreal Lecture Notes by the first author [Théorie asymptotique de la decision statistique. (1969; Zbl 0374.62024)]. They have been updated by remarks concerning some new developments like LAMN-structures or nonparametric LAN-cases. The book does not contain full proofs of all main theorems nor does it present a coherent introduction into the subject. It gives some impression of what type of mathematics one has to expect when reading the big monograph of L. Le Cam, Asymptotic methods in statistical decision theory. (1986; Zbl 0605.62002). At first reading one should be well aquainted with classical asymptotics since the authors tend to worry about nonregular cases instead of presenting the stream-lined examples.
Reviewer: H.Strasser (Wien)

62-02 Research exposition (monographs, survey articles) pertaining to statistics
62E20 Asymptotic distribution theory in statistics
62F05 Asymptotic properties of parametric tests
62F12 Asymptotic properties of parametric estimators
62G20 Asymptotic properties of nonparametric inference
62C99 Statistical decision theory
60F99 Limit theorems in probability theory