Cover of: U-Statistics in Banach Spaces | Yu. V. Borovskikh

U-Statistics in Banach Spaces

  • 420 Pages
  • 1.44 MB
  • English
Brill Academic Publishers
Functional analysis, Probability & statistics, Banach Spaces, Mathematics, Architecture, Science/Mathematics, General, Interior Design - General, Geometry - Ge
The Physical Object
ID Numbers
Open LibraryOL12849182M
ISBN 109067642002
ISBN 139789067642002

U-Statistics in Banach Spaces book situation when the kernel of a U-statistic takes values in a Banach space, turns out to be the most natural and interesting. In this book, the author presents in a systematic form the probabilistic theory of U-statistics with values in Banach spaces (UB-statistics), which has been developed to by:   U-statistics in Banach spaces are considered and thoroughly investigated.

The martingale structure, estimates of moments, the law of large numbers, the central limit theorem, the invariance principle, estimates of the rate of convergence, and large deviations are Cited by: U-statistics are universal objects of modern probabilistic summation theory.

This book systematically presents the probabilistic theory of U-statistics with values in Banach spaces (UB-statistics), Read more.

In this book, the author presents in a systematic form the probabilistic theory of U-statistics with values in Banach spaces (UB-statistics), which has been developed to date. U-statistics are very natural in statistical work, particularly in Hoeffding's context of independent and identically-distributed random variables, or more generally for exchangeable sequences, such as in simple random sampling from a finite population, U-statistics in Banach spaces.

Utrecht: VSP. xii+ In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X 1, X 2, X 3, (which may be finitely or infinitely long) whose joint probability distribution does not change when the positions in the sequence in which finitely many of them appear are altered.

Thus, for example the sequences,, both have the same joint probability. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 's and developed strongly in the 's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis.

Get this from a library. Probability in Banach spaces, 8: proceedings of the eighth international conference. [R M Dudley; Marjorie G Hahn; James Kuelbs;] -- Probability limit theorems in infinite-dimensional spaces give conditions unƯ der which convergence holds uniformly over an infinite class of sets or functions.

Early results in this direction were. [2] Yu. Borovskikh., U-Statistics in Banach Spaces.V.S.P. Intl Science, [3] Leo Breiman. Bagging predictors., Machine Learning, –, Cited by: 3. Probability limit theorems in infinite-dimensional spaces give conditions un­ der which convergence holds uniformly over an infinite class of sets or functions.

Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions.

The autoregressive model in a Banach space (ARB) allows to represent many continuous time processes used in practice (see, for example, D. Bosq. Svante Janson (born 21 May ) is a Swedish mathematician.A member of the Royal Swedish Academy of Sciences sinceJanson has been the chaired professor of mathematics at Uppsala University since In mathematical analysis, Janson has publications in functional analysis (especially harmonic analysis) and probability mathematical statistics, Alma mater: Uppsala University.

The law of the iterated logarithm for canonical or completely degenerate U-statistics with square integrable kernel h is proved, for h taking values in, and, in general, in a type 2 separable.

Credit Hours: 3; Course Summary: Completeness of the real number system, basic topological properties, compactness, sequences and series, absolute convergence of series, rearrangement of series, properties of continuous functions, the Riemann-Stieltjes integral, sequences and series of functions, uniform convergence, the Stone-Weierstrass theorem, equicontinuity, and the.

Marcinkiewicz type laws of large numbers and convergence of moments for U-statistics. Probability in Banach Spaces 8 – Birkhäuser, Boston.

Description U-Statistics in Banach Spaces FB2

zbMATH Google Scholar. As an application of this approach we present a new two sided decoupling inequality for a class of generalized U-statistics taking values in a separable Banach space.

A.M.S.\ () subject classification:60E15, 46E Key words and Phrases:\ \ Multilinear Forms, U-Statistics, Rearrangement Invariant Spaces, Decoupling, Tail Probabilities. Presnell B and Bohn L U Statistics and Imperfect Ranking in Ranked Set from STA at University of Florida.

Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange. From banach-request at Tue Feb 2 To: banach-dist at Subject: Abstract of a paper by i and n Date: Tue, 2 Feb 93 CST From: alspach at Sender: alspach at Content-Length: X-Lines: 21 Status: RO This is the abstract of the.

statistics and UB− statistics for arbitrary (separable) Banach space valued statis-tics. The case of the Banach spaces with smooth norm and the Banach spaces of a finite type (co - type) p, p≥ 1 was considered in the books [17], [3]. Note that the case d= r= Author: E.

Ostrovsky, L. Sirota. Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference by R. Dudley,available at Book Depository with free delivery worldwide. The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem.

During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces.

The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, on approximation and wavelet theory, and on the basic theory of function by: Geometric median and robust estimation in Banach spaces.

Bernoulli 21 – Zentralblatt MATH: Digital Object Identifier: doi/BEJ Project Euclid: by: 8. In their Preface, the editors suggest that a good source for understanding the field of probability in Banach spaces is the book by M.

Ledoux and M. Talagrand (Probability in Banach Spaces, Springer, Berlin, ). Several im- portant papers by Talagrand have also appeared after () Invariance principles for U-statistics and von mises functionals.

Journal of Statistical Planning and Inference() A bounded law of the iterated logarithm for Hilbert space valued martingales and its application to by:   This includes the areas of probability in Banach spaces; empirical process theory; asymptotic theory of the bootstrap and of U-statistics and processes; as well as nonparametric statistics.

He wrote over articles in leading scientific journals: 22 papers in the Annals of Probability alone, 10 in Probability Theory and Related Fields, and 8. probability in Banach spaces, empirical processes, the bootstrap, U-statistics and processes, and mathematical statistics.

We refer to the editorial of this memorial volume for a biographical summary of Evarist’s life. A list of all of Evarist’s publications, including his three books, can be found at the end of this article. Decoupling: From Dependence to Independence - Ebook written by Victor de la Peña, Evarist Giné.

Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Decoupling: From Dependence to Independence.

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Probability in Banach Spaces, 9, () Central limit theorems for empirical andU-processes of stationary mixing sequences. Journal of Theoretical ProbabilityCited by:. BOOK REVIEW: Quasi-Likelihood and Its Application, by Christopher C. Heyde Jordan Stoyanov.

Back to contents. Volume 11 Issue 4. Self-Similar Processes in Collective Risk Theory Zbigniew Michna. Volterra and Urysohn Integral Equations in Banach Spaces Donal O'Regan.

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Moment Computation in Shift Invariant Spaces compare. The theory of decoupling inequalities developed originally in the study of Banach spaces, stochastic processes, and U-statistics, mainly between the mid-’80s and mid-’90s; see [dlPG99] for a book-length treatment.

The powerful tool of decoupling seems to be relatively under-used in theoretical computer science.InEvarist began to publish on central limit theorems in Banach spaces.

I think since then, he (and others) had known more than I do about limit theorems in separable Banach spaces. Araujo and Giné was a book on such central limit theorems.

The book is by far Evarist’s most cited work (Google Scholar).Author: R.M. Dudley.