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One-dimensional empirical measures, order statistics, and Kantorovich transport distances
This work is devoted to the study of rates of convergence of the empirical measures \\mu_{n} = \\frac {1}{n} \\sum_{k=1}^n \\delta_{X_k}, n \\geq 1, over a sample (X_{k})_{k \\geq 1} of independent identically distributed real-valued random variables towards the common distribution \\mu in Kantorovich transport distances W_p. The focus is on finite range bounds on the expected Kantorovich distances \\mathbb{E}(W_{p}(\\mu_{n},\\mu )) or \\big [ \\mathbb{E}(W_{p}^p(\\mu_{n},\\mu )) \\big ]^1/p in terms of moments and analytic conditions on the measure \\mu and its distribution function. The study describes a variety of rates, from the standard one \\frac {1}{\\sqrt n} to slower rates, and both lower and upper-bounds on \\mathbb{E}(W_{p}(\\mu_{n},\\mu )) for fixed n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.
eBook
Additive Differentials for ARX Mappings with ProbabilityExceeding 1/4
We consider the additive differential probabilities of functions and , where and . The probabilities are used for the differential cryptanalysis of ARX ciphers that operate only with addition modulo , bitwise XOR ( ), and bit rotations ( ). A complete characterization of differentials whose probability exceeds is obtained. All possible values of their probabilities are for . We describe differentials with each of these probabilities and calculate the number of these values. We also calculate the number of all considered differentials. It is for and for , where . We compare differentials of both mappings under the given constraint.
Journal Article
Common errors in statistics (and how to avoid them)
\"The Fourth Edition of this tried-and-true book elaborates on many key topics such as epidemiological studies, distribution of data; baseline data incorporation; case control studies; simulations; statistical theory publication; biplots; instrumental variables; ecological regression; result reporting, survival analysis; etc. Including new modifications and figures, the book also covers such topics as research plan creation; data collection; hypothesis formulation and testing; coefficient estimates; sample size specifications; assumption checking; p-values interpretations and confidence intervals; counts and correlated data; model building and testing; Bayes' Theorem; bootstrap and permutation tests; and more\"-- Provided by publisher.
Book
Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits
We study a class of measure-theoretic objects that we call
eBook
A practical introduction to index numbers
\"This book offers an introduction to the subject of index numbers for statisticians, economists and numerate members of the public\"-- Provided by publisher.
Book
The Pseudo-Marginal Approach for Efficient Monte Carlo Computations
We introduce a powerful and flexible MCMC algorithm for stochastic simulation. The method builds on a pseudo-marginal method originally introduced in [Genetics 164 (2003) 1139-1160], showing how algorithms which are approximations to an idealized marginal algorithm, can share the same marginal stationary distribution as the idealized method. Theoretical results are given describing the convergence properties of the proposed method, and simple numerical examples are given to illustrate the promising empirical characteristics of the technique. Interesting comparisons with a more obvious, but inexact, Monte Carlo approximation to the marginal algorithm, are also given.
Journal Article
Handbook of regression analysis
\"Written by two established experts in the field, the purpose of this handbook is to provide a practical, one-stop reference on regression analysis. The focus is on the tools that both practitioners and researchers use in real life. It is intended to be a comprehensive collection of the theory, methods, and applications of the subject matter, but it is deliberately written at an accessible level. The handbook will provide a quick and convenient reference or \"refresher\" on ideas and methods that are useful for the accurate analysis of data and its resulting interpretations. Students can use the book as an introduction to and/or summary of key concepts in regression and related course work (such as linear, nonlinear, and nonparametric regressions). Plentiful references are supplied for the more motivated readers. Theory is presented when necessary, and always supplemented by hands-on examples. Software routines are available via an author-maintained web site\"-- Provided by publisher.
Book
Symmetric Markov processes, time change, and boundary theory
This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elements and applications of the theory of symmetric Markov processes, including recurrence/transience criteria, probabilistic potential theory, additive functional theory, and time change theory. The authors develop the theory in a general framework of symmetric quasi-regular Dirichlet forms in a unified manner with that of regular Dirichlet forms, emphasizing the role of extended Dirichlet spaces and the rich interplay between the probabilistic and analytic aspects of the theory. Chen and Fukushima then address the latest advances in the theory, presented here for the first time in any book. Topics include the characterization of time-changed Markov processes in terms of Douglas integrals and a systematic account of reflected Dirichlet spaces, and the important roles such advances play in the boundary theory of symmetric Markov processes.
This volume is an ideal resource for researchers and practitioners, and can also serve as a textbook for advanced graduate students. It includes examples, appendixes, and exercises with solutions.
eBook