Gaussian measures and processes sample continuity 3. Foundations of uniform central limit theorems: Donsker classes 4. Weak convergences of marked empirical processes in a Hilbert space and their applications.
Local Rademacher complexities and oracle inequalities in risk minimization. Given a sample X 1 , View 5 excerpts, cites background and methods. Lithuanian Mathematical Journal. Let X, X1, X2,. Gaussian approximation of suprema of empirical processes.
We develop a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating empirical processes … Expand.
View 3 excerpts, cites background. Related Papers. Abstract 5, Citations Related Papers. By clicking accept or continuing to use the site, you agree to the terms outlined in our Privacy Policy , Terms of Service , and Dataset License. The weak convergence theory developed in Part 1 is important for this, simply because the empirical processes studied in Part 2, Empirical Processes, are naturally viewed as taking values in nonseparable Banach spaces, even in the most elementary cases, and are typically not Borel measurable.
Much of the theory presented in Part 2 has previously been scattered in the journal literature and has, as a result, been accessible only to a relatively small number of specialists. Authors and affiliations Aad W. Wellner 2 1. The main purpose of this paper is to investigate the strong approximation of the p-fold integrated empirical process, p being a fixed positive integer. More precisely, we obtain the exact rate of the … Expand.
Highly Influenced. View 6 excerpts, cites methods, results and background. Asymptotic results for hybrids of empirical and partial sums processes. The present paper is devoted to the study of the hybrids of empirical and partial sums processes. In the first part, we present a synthesis of results related to these processes and their connection … Expand.
On the strong approximation of bootstrapped empirical copula processes with applications. The purpose of the present paper is to provide a strong invariance principle for the generalized bootstrapped empirical copula processwith the rate of the approximation for multivariate empirical … Expand.
Asymptotics via Empirical Processes. This paper offers a glimpse into the theory of empirical processes. Two asymptotic problems are sketched as motivation for the study of maximal inequalities for stochastic processes made up of … Expand.
In order to evaluate the limiting laws, a general notion of … Expand. Gaussian approximation of local empirical processes indexed by functions. An extended notion of a local empirical process indexed by functions is introduced, which includes kernel density and regression function estimators and the conditional empirical process as … Expand.
Quantile processes with statistical applications. Independence Empirical Processes. The Delta-Method. Previous Page 2 Navigate to page number of 3. About this book Introduction This book tries to do three things. The first goal is to give an exposition of certain modes of stochastic convergence, in particular convergence in distribution.
The classical theory of this subject was developed mostly in the s and is well summarized in Billingsley During the last 15 years, the need for a more general theory allowing random elements that are not Borel measurable has become well established, particularly in developing the theory of empirical processes. Part 1 of the book, Stochastic Convergence, gives an exposition of such a theory following the ideas of J.
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