×

A note on the Hájek-LeCam bound. (English) Zbl 0934.62010

Summary: Let \(E_n\) be a sequence of experiments weakly converging to a limit experiment \(E\). One of the basic objectives of asymptotic decision theory is to derive asymptotically “best” decisions in \(E_n\) from optimal decisions in the limit experiment \(E\). A central statement in this context is the Hájek-LeCam bound which is an asymptotic lower bound for the maximum risk of a sequence of decisions. To give a simplified proof for the Hájek-LeCam bound we use the concept of approximate Blackwell-sufficiency.

MSC:

62B15 Theory of statistical experiments
62B05 Sufficient statistics and fields
PDFBibTeX XMLCite
Full Text: EuDML Link

References:

[1] I. Csiszár: Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität Markoffscher Ketten. Publ. Math. Inst. Hungar. Acad. Sci., Ser. A, 8 (1963), 85-108. · Zbl 0124.08703
[2] L. LeCam: Asymptotic Methods in Statistical Decision Theory. Springer-Verlag, Berlin–Heidelberg–New York 1986.
[3] F. Liese, I. Vajda: Convex Statistical Distances. Teubner Verlag, Leipzig 1987. · Zbl 0656.62004
[4] P. W. Millar: The minimax principle in asymptotic statistical theory. Lecture Notes in Mathematics 974, pp. 75-265. Springer-Verlag, Berlin–Heidelberg–New York 1983. · Zbl 0502.62027
[5] G. Neuhaus: Einige Kapitel der finiten und asymptotischen Entscheidungstheorie von LeCam. Hamburg 1989. · Zbl 0689.62007
[6] L. Rüschendorf: Asymptotische Statistik. Skripten zur Mathematischen Statistik Nr. 13, Münster 1987. · Zbl 0661.62001
[7] H. Strasser: Mathematical Theory of Statistics. de Gruyter, Berlin 1985. · Zbl 0594.62017 · doi:10.1515/9783110850826
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.