Conditionally Independent Sequences
Chapter 6 was devoted to the study of the general properties of tangent sequences. In particular, in Sections 6.3 and 6.4 results were presented for comparing the tail probabilities and moments of tangent sequences when the variables involved are non-negative, conditionally symmetric, or form a martingale difference sequence. Two results from that chapter (Corollary 6.2.5 and Corollary 6.4.3) dealt with comparisons between the moment generating function and the 4-norm of an arbitrary sum and its decoupled (conditionally independent) counterpart. In this chapter we continue to study this type of comparison. The main advantage realized is in the increased accuracy of the results obtained which in several problems translates into the almost direct transfer of results for sums of independent random variables to the case of sums of dependent random variables.
KeywordsCentral Limit Theorem Independent Random Variable Tail Probability Dependent Random Variable Independent Sequence
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