The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
Harro Walk - One of the best experts on this subject based on the ideXlab platform.
-
Estimation of the essential supremum of a regression function
Statistics & Probability Letters, 2011Co-Authors: Michael Köhler, Adam Krzyżak, Harro WalkAbstract:Given an independent and identically distributed sample of the distribution of an -valued random vector (X,Y), the problem of estimation of the essential supremum of the corresponding regression function is considered. Estimates are constructed, which converge almost surely to this value whenever the dependent variable Y satisfies some weak Integrability Condition.
-
Estimation of the essential supremum of a regression function
Statistics & Probability Letters, 2011Co-Authors: Michael Köhler, Adam Krzyżak, Harro WalkAbstract:Abstract Given an independent and identically distributed sample of the distribution of an R d × R -valued random vector ( X , Y ) , the problem of estimation of the essential supremum of the corresponding regression function m ( x ) = E { Y | X = x } is considered. Estimates are constructed, which converge almost surely to this value whenever the dependent variable Y satisfies some weak Integrability Condition.
Yan Liang - One of the best experts on this subject based on the ideXlab platform.
-
Fatou's Lemma for Weakly Converging Measures under the Uniform Integrability Condition
Theory of Probability & Its Applications, 2020Co-Authors: Eugene A Feinberg, Pavlo O. Kasyanov, Yan LiangAbstract:This paper describes Fatou's lemma for a sequence of measures converging weakly to a finite measure and for a sequence of functions whose negative parts are uniformly integrable with respect to the...
-
Fatou's lemma for weakly converging measures under the uniform Integrability Condition
Teoriya Veroyatnostei i ee Primeneniya, 2019Co-Authors: Евгений Александрович Файнберг, Eugene A Feinberg, Yan Liang, Павел Олегович Касьянов, Pavel Olegovich Kas'yanovAbstract:В статье устанавливаются лемма Фату и теорема Лебега о мажорируемой сходимости для слабо сходящихся последовательностей конечных мер и равномерно интегрируемых по этим мерам функций. Заметка содержит также новые формулировки равномерной леммы Фату, равномерной теоремы Лебега о мажорируемой сходимости, теоремы Данфорда-Петтиса и фундаментальной теоремы о мерах Янга, основанные на эквивалентности условия равномерной интегрируемости и кажущегося более слабым условия асимптотической равномерной интегрируемости для последовательностей функций и конечных мер.
-
Fatou's Lemma for Weakly Converging Measures under the Uniform Integrability Condition
arXiv: Classical Analysis and ODEs, 2018Co-Authors: Eugene A Feinberg, Pavlo O. Kasyanov, Yan LiangAbstract:This note describes Fatou's lemma and Lebesgue's dominated convergence theorem for a sequence of measures converging weakly to a finite measure and for a sequence of functions whose negative parts are uniformly integrable with respect to these measures. The note also provides new formulations of uniform Fatou's lemma, uniform Lebesgue convergence theorem, the Dunford-Pettis theorem, and the fundamental theorem for Young measures based on the equivalence of uniform Integrability and the apparently weaker property of asymptotic uniform Integrability for sequences of functions and finite measures.
Michael Köhler - One of the best experts on this subject based on the ideXlab platform.
-
Estimation of the essential supremum of a regression function
Statistics & Probability Letters, 2011Co-Authors: Michael Köhler, Adam Krzyżak, Harro WalkAbstract:Given an independent and identically distributed sample of the distribution of an -valued random vector (X,Y), the problem of estimation of the essential supremum of the corresponding regression function is considered. Estimates are constructed, which converge almost surely to this value whenever the dependent variable Y satisfies some weak Integrability Condition.
-
Estimation of the essential supremum of a regression function
Statistics & Probability Letters, 2011Co-Authors: Michael Köhler, Adam Krzyżak, Harro WalkAbstract:Abstract Given an independent and identically distributed sample of the distribution of an R d × R -valued random vector ( X , Y ) , the problem of estimation of the essential supremum of the corresponding regression function m ( x ) = E { Y | X = x } is considered. Estimates are constructed, which converge almost surely to this value whenever the dependent variable Y satisfies some weak Integrability Condition.
Wolfgang Wefelmeyer - One of the best experts on this subject based on the ideXlab platform.
-
On efficient estimation of densities for sums of squared observations
Statistics & Probability Letters, 2012Co-Authors: Anton Schick, Wolfgang WefelmeyerAbstract:Abstract Densities of functions of independent and identically distributed random observations can be estimated by using a local U -statistic. Under an appropriate Integrability Condition, this estimator behaves asymptotically like an empirical estimator. In particular, it converges at the parametric rate. The Integrability Condition is rather restrictive. It fails for the sum of powers of two observations when the exponent is at least 2. We have shown elsewhere that for the exponent equal to 2 the rate of convergence slows down by a logarithmic factor in the support of the squared observation. Here we show that the estimator is efficient in the sense of Hajek and Le Cam. In particular, the convergence rate is optimal.
Adam Krzyżak - One of the best experts on this subject based on the ideXlab platform.
-
Estimation of the essential supremum of a regression function
Statistics & Probability Letters, 2011Co-Authors: Michael Köhler, Adam Krzyżak, Harro WalkAbstract:Given an independent and identically distributed sample of the distribution of an -valued random vector (X,Y), the problem of estimation of the essential supremum of the corresponding regression function is considered. Estimates are constructed, which converge almost surely to this value whenever the dependent variable Y satisfies some weak Integrability Condition.
-
Estimation of the essential supremum of a regression function
Statistics & Probability Letters, 2011Co-Authors: Michael Köhler, Adam Krzyżak, Harro WalkAbstract:Abstract Given an independent and identically distributed sample of the distribution of an R d × R -valued random vector ( X , Y ) , the problem of estimation of the essential supremum of the corresponding regression function m ( x ) = E { Y | X = x } is considered. Estimates are constructed, which converge almost surely to this value whenever the dependent variable Y satisfies some weak Integrability Condition.