Theory and applications of multivariate self-normalized processes

Victor H. de la Peña, Michael J. Klass and Tze Leung Lai

Stochastic Processes and their Applications, 2009, vol. 119, issue 12, 4210-4227

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.

Keywords: Matrix; normalization; Method; of; mixtures; Moment; and; exponential; inequalities; Martingales (search for similar items in EconPapers)
Date: 2009
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