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Conditional independence, conditional mixing and conditional association

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Abstract

Some properties of conditionally independent random variables are studied. Conditional versions of generalized Borel-Cantelli lemma, generalized Kolmogorov’s inequality and generalized Hájek-Rényi inequality are proved. As applications, a conditional version of the strong law of large numbers for conditionally independent random variables and a conditional version of the Kolmogorov’s strong law of large numbers for conditionally independent random variables with identical conditional distributions are obtained. The notions of conditional strong mixing and conditional association for a sequence of random variables are introduced. Some covariance inequalities and a central limit theorem for such sequences are mentioned.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Hyderabad, Hyderabad, 500 046, India

    B. L. S. Prakasa Rao

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  1. B. L. S. Prakasa Rao
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Correspondence to B. L. S. Prakasa Rao.

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Prakasa Rao, B.L.S. Conditional independence, conditional mixing and conditional association. Ann Inst Stat Math 61, 441–460 (2009). https://doi.org/10.1007/s10463-007-0152-2

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  • DOI: https://doi.org/10.1007/s10463-007-0152-2

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