Asymptotics: particles, processes, and inverse problems: by Eric A. Cator, Cor Kraaikamp, Hendrik P. Lopuhaa, Jon A.

By Eric A. Cator, Cor Kraaikamp, Hendrik P. Lopuhaa, Jon A. Wellner, Geurt Jongbloed

Cator E.A., et al. (eds.) Asymptotics.. debris, procedures and inverse difficulties (Inst.Math.Stat., 2007)(ISBN 0940600714)-o

Show description

Read or Download Asymptotics: particles, processes, and inverse problems: festschrift for Piet Groeneboom PDF

Best probability books

Credit Risk: Modeling, Valuation and Hedging

The most goal of credits possibility: Modeling, Valuation and Hedging is to provide a finished survey of the earlier advancements within the sector of credits chance examine, in addition to to place forth the latest developments during this box. a major element of this article is that it makes an attempt to bridge the distance among the mathematical conception of credits hazard and the monetary perform, which serves because the motivation for the mathematical modeling studied within the publication.

Meta Analysis: A Guide to Calibrating and Combining Statistical Evidence

Meta research: A consultant to Calibrating and mixing Statistical facts acts as a resource of uncomplicated equipment for scientists desirous to mix proof from varied experiments. The authors objective to advertise a deeper knowing of the concept of statistical proof. The ebook is made from components - The instruction manual, and the idea.

Measures, integrals and martingales

This can be a concise and easy advent to modern degree and integration thought because it is required in lots of components of research and chance idea. Undergraduate calculus and an introductory direction on rigorous research in R are the single crucial must haves, making the textual content compatible for either lecture classes and for self-study.

Stochastic Digital Control System Techniques

''This e-book might be an invaluable connection with regulate engineers and researchers. The papers contained conceal good the hot advances within the box of contemporary keep watch over thought. ''- IEEE team Correspondence''This publication may also help all these researchers who valiantly try and maintain abreast of what's new within the concept and perform of optimum keep an eye on.

Additional resources for Asymptotics: particles, processes, and inverse problems: festschrift for Piet Groeneboom

Example text

Jongbloed, G. and Wellner, J. A. (2001). Estimation of a convex function: characterizations and asymptotic theory. Ann. Statist. 29 1653–1698. MR1891742 [12] Hall, C. A. (1968). On error bounds for spline interpolation. J. Approximation Theory 1 209–218. MR0239324 [13] Hall, C. A. and Meyer, W. W. (1976). Optimal error bounds for cubic spline interpolation. J. Approximation Theory 16 105–122. MR0397247 [14] Kiefer, J. and Wolfowitz, J. (1976). Asymptotically minimax estimation of concave and convex distribution functions.

Asymptotically minimax estimation of concave and convex distribution functions. Z. Wahrsch. Verw. Gebiete 34 73–85. MR0397974 [15] Kiefer, J. and Wolfowitz, J. (1977). Asymptotically minimax estimation of concave and convex distribution functions. II. In Statistical Decision Theory and Related Topics. II (Proc. , 1976) 193–211. Academic Press, New York. MR0443202 ¨, H. P. (2006). The limit process of the dif[16] Kulikov, V. N. and Lopuhaa ference between the empirical distribution function and its concave majorant.

This implies the claimed bound. Main steps: A. By Marshall’s lemma, for any concave function h, Fn − h ≤ Fn − h . (k ) B. PF (An ) ≡ PF {Ln n is concave on [0, ∞)} ր 1 as n → ∞ if kn ≡ (C0 β1 (F )× 1/3 n/ log n) for some absolute constant C0 . C. On the event An , it follows from Marshall’s lemma (step A) that n) n) + L(k − Fn Fn − Fn = Fn − L(k n n (kn ) (kn ) ≤ Fn − Ln + Ln − Fn n) = 2 Fn − L(k n n) = 2 Fn − L(k − (F − L(kn ) ) + F − L(kn ) ) n n) ≤ 2 Fn − L(k − (F − L(kn ) ) + 2 F − L(kn ) n ≡ 2(Dn + En ).

Download PDF sample

Rated 4.20 of 5 – based on 22 votes