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Strong Law of Large Numbers with Operator Normalizations for Martingales and Sums of Orthogonal Random Vectors

We establish the strong law of large numbers with operator normalizations for vector martingales and sums of orthogonal random vectors. We describe its applications to the investigation of the strong consistency of least-squares estimators in a linear regression and the asymptotic behavior of multid...

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Date:2000
Main Authors: Buldygin, V. V., Koval, V. A., Булдыгин, В. В., Коваль, В. А.
Format: Article
Language:Russian
English
Published: Institute of Mathematics, NAS of Ukraine 2000
Online Access:https://umj.imath.kiev.ua/index.php/umj/article/view/4508
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Journal Title:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
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author Buldygin, V. V.
Koval, V. A.
Булдыгин, В. В.
Коваль, В. А.
Булдыгин, В. В.
Коваль, В. А.
author_facet Buldygin, V. V.
Koval, V. A.
Булдыгин, В. В.
Коваль, В. А.
Булдыгин, В. В.
Коваль, В. А.
author_sort Buldygin, V. V.
baseUrl_str https://umj.imath.kiev.ua/index.php/umj/oai
collection OJS
datestamp_date 2020-03-18T20:30:18Z
description We establish the strong law of large numbers with operator normalizations for vector martingales and sums of orthogonal random vectors. We describe its applications to the investigation of the strong consistency of least-squares estimators in a linear regression and the asymptotic behavior of multidimensional autoregression processes.
first_indexed 2026-03-24T03:00:13Z
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publisher Institute of Mathematics, NAS of Ukraine
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spelling umjimathkievua-article-45082020-03-18T20:30:18Z Strong Law of Large Numbers with Operator Normalizations for Martingales and Sums of Orthogonal Random Vectors Усиленный закон больших чисел с операторными нормировками для мартингалов и сумм ортогональных случайных векторов Buldygin, V. V. Koval, V. A. Булдыгин, В. В. Коваль, В. А. Булдыгин, В. В. Коваль, В. А. We establish the strong law of large numbers with operator normalizations for vector martingales and sums of orthogonal random vectors. We describe its applications to the investigation of the strong consistency of least-squares estimators in a linear regression and the asymptotic behavior of multidimensional autoregression processes. Встановлено підсилений закон великих чисел з операторними нормуваннями для векторних мартингалів та сум ортогональних випадкових векторів. Наведено його застосування до дослідження сильної слушності оцінок найменших квадратів в лінійній регресії та асимптотичної поведінки багатовимірних процесів авторегресії. Institute of Mathematics, NAS of Ukraine 2000-08-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4508 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 8 (2000); 1045-1061 Український математичний журнал; Том 52 № 8 (2000); 1045-1061 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4508/5720 https://umj.imath.kiev.ua/index.php/umj/article/view/4508/5721 Copyright (c) 2000 Buldygin V. V.; Koval V. A.
spellingShingle Buldygin, V. V.
Koval, V. A.
Булдыгин, В. В.
Коваль, В. А.
Булдыгин, В. В.
Коваль, В. А.
Strong Law of Large Numbers with Operator Normalizations for Martingales and Sums of Orthogonal Random Vectors
title Strong Law of Large Numbers with Operator Normalizations for Martingales and Sums of Orthogonal Random Vectors
title_alt Усиленный закон больших чисел с операторными нормировками для мартингалов и сумм ортогональных случайных векторов
title_full Strong Law of Large Numbers with Operator Normalizations for Martingales and Sums of Orthogonal Random Vectors
title_fullStr Strong Law of Large Numbers with Operator Normalizations for Martingales and Sums of Orthogonal Random Vectors
title_full_unstemmed Strong Law of Large Numbers with Operator Normalizations for Martingales and Sums of Orthogonal Random Vectors
title_short Strong Law of Large Numbers with Operator Normalizations for Martingales and Sums of Orthogonal Random Vectors
title_sort strong law of large numbers with operator normalizations for martingales and sums of orthogonal random vectors
url https://umj.imath.kiev.ua/index.php/umj/article/view/4508
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