Strong Laws for L- and U-statistics
نویسندگان
چکیده
Strong laws of large numbers are given for L-statistics (linear com binations of order statistics) and for U -statistics (averages of kernels of ran dom samples) for ergodic stationary processes, extending classical theorems of Hoeffding and of Helmers for iid sequences. Examples are given to show that strong and even weak convergence may fail if the given sufficient conditions are not satisfied, and an application is given to estimation of correlation dimension of invariant measures.
منابع مشابه
Sub-bernoulli Functions, Moment Inequalities and Strong Laws for Nonnegative and Symmetrized
This paper concerns moment and tail probability inequalities and the strong law of large numbers for U-statistics with nonnegative or symmetrized kernels and their multisample and decoupled versions. SubBernoulli functions are used to obtain the moment and tail probability inequalities, which are then used to obtain necessary and sufficient conditions for the almost sure convergence to zero of ...
متن کاملImproving Symptoms of Primary Sclerosing Cholangitis by Iranian Traditional Medicine
Introduction: Primary Sclerosing Cholangitis (PSC) is a chronic cholestatic disease that results from the inflammation and destruction of intra- and extra-hepatic bile ducts and fibrosis which can lead to cirrhosis. The purpose of this report is to provide the clinical experience of Iranian traditional medicine with the best therapeutic effect within the shortest time. <s...
متن کاملStrong traces for solutions to scalar conservation laws with general flux
In this paper we consider bounded weak solutions u of scalar conservation laws, not necessarily of class BV , defined in a subset Ω ⊂ R+×R. We define a strong notion of trace at the boundary of Ω reached by L convergence for a large class of functionals of u, G(u). Those functionals G depend on the flux function of the conservation law and on the boundary of Ω. The result holds for general flux...
متن کاملImm-s) ^ I Limit Laws for Extreme Order Statistics from Strong-mixing Processes"''
This paper considers the possible limit laws for a sequence of normalized extreme order statistics (maximum, second maximum, etc.) from a stationary strong-mixing sequence of random variables. It extends the work of Loynes who treated only the maximum process. The maximum process leads to limit laws that are the same three types that occur when the underlying process is a sequence of independen...
متن کاملFe b 20 07 Uniform in bandwidth consistency of conditional U - statistics
In 1991 Stute introduced a class of estimators called conditional U –statistics. They can be seen as a generalization of the Nadaraya-Watson estimator for the regression function, and he proved their strong pointwise consistency to Very recently, Giné and Mason introduced the notion of a local U –process, which generalizes that of a local empirical process, and obtained central limit theorems a...
متن کامل