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- W2034709788 abstract "Multivariate self-normalized processes, for which self-normalization consists of multiplying by the inverse of a positive definite matrix (instead of dividing by a positive random variable as in the scalar case), are ubiquitous in statistical applications. In this paper we make use of a technique called “pseudo-maximization” to derive exponential and moment inequalities, and bounds for boundary crossing probabilities, for these processes. In addition, Strassen-type laws of the iterated logarithm are developed for multivariate martingales, self-normalized by their quadratic or predictable variations." @default.
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- W2034709788 date "2009-12-01" @default.
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- W2034709788 title "Theory and applications of multivariate self-normalized processes" @default.
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- W2034709788 doi "https://doi.org/10.1016/j.spa.2009.10.003" @default.
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