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Convergence rates for sequences of conditionally independent and conditionally identically distributed random variables

De-Mei Yuan
대한수학회 (The Korean Mathematical Society)|2016.11|대한수학회지 (Journal of the KMS)|제53권 제6호|pp. 1275-1292

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참고문헌

키워드

conditional independenceconditionally identical distributivenessconditional medianconditional symmetrization inequality
주제분류수학

초록

The Marcinkiewicz-Zygmund strong law of large numbers for conditionally independent and conditionally identically distributed random variables is an existing, but merely qualitative result. In this paper, for the more general cases where the conditional order of moment belongs to $\left({0,\infty } \right)$ instead of $\left( {0,2} \right)$, we derive results on convergence rates which are quantitative ones in the sense that they tell us how fast convergence is obtained. Furthermore, some conditional probability inequalities are of independent interest.

Abstract

The Marcinkiewicz-Zygmund strong law of large numbers for conditionally independent and conditionally identically distributed random variables is an existing, but merely qualitative result. In this paper, for the more general cases where the conditional order of moment belongs to $\left({0,\infty } \right)$ instead of $\left( {0,2} \right)$, we derive results on convergence rates which are quantitative ones in the sense that they tell us how fast convergence is obtained. Furthermore, some conditional probability inequalities are of independent interest.

참고문헌 (22)

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  20. De-Mei Yuan, "EXTENSIONS OF SEVERAL CLASSICAL RESULTS FOR INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES TO CONDITIONAL CASES", 대한수학회지, 52(2), pp.431~445 (2015), 대한수학회
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관련 논문AI추천

EXTENSIONS OF SEVERAL CLASSICAL RESULTS FOR INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES TO CONDITIONAL CASESDe-Mei Yuan, Shun-Jing Li대한수학회 · 대한수학회지2015 · 제52권 제2호A strong limit theorem for sequences of blockwise and pairwise m-dependent random variablesNgoc Anh Vu, Van Thanh Le대한수학회 · 대한수학회보2011 · 제48권 제2호ON COMPLETE CONVERGENCE AND COMPLETE MOMENT CONVERGENCE FOR A CLASS OF RANDOM VARIABLESXuejun Wang, Yi Wu대한수학회 · 대한수학회지2017 · 제54권 제3호Central limit theorems for conditionally strong mixing and conditionally strictly stationary sequences of random variablesDe-Mei Yuan, Xiao-Lin Zeng대한수학회 · 대한수학회지2024 · 제61권 제4호On complete convergence for weighted sums of i.i.d. random variables with application to moving average processesSoo Hak Sung대한수학회 · 대한수학회보2009 · 제46권 제4호On the complete convergence for weighted sums of dependent random variables under condition of weighted integrabilityJong-Il Baek, Mi-Hwa Ko, Tae-Sung Kim대한수학회 · 대한수학회지2008 · 제45권 제4호

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