Multivariate Theory for Analyzing High Dimensional Data

By Muni S. Srivastava. 2007

141 citations recorded by the source corpus.

In this article, we develop a multivariate theory for analyzing multivariate datasets that have fewer observations than dimensions. More specifically, we consider the problem of testing the hypothesis that the mean vector µ of a p-dimensional random vector x is a zero vector where N, the number of independent observations on x, is less than the dimension p. It is assumed that x is normally distributed with mean vector µ and unknown nonsingular covariance matrix Σ. We propose the

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b725e3c37b3acbbc03562fc3595a9e127130d03f

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Citations in the corpus

On the Behrens–Fisher problem: A globally convergent algorithm and a finite-sample study of the Wald, LR and LM tests (2008, background): “In recent years, interesting applied problems have been found which can be formulated, in a generic sense, in the framework of the Behrens–Fisher Prob-lem under high dimension and low sample size (see, e.g., Srivastava [31]).”
RAPTT: An Exact Two-Sample Test in High Dimensions Using Random Projections (2014, methodology): “In an earlier work, Srivastava (2007) modiﬁed the T 2 statistic by replacing the inverse of S with the Moore-Penrose inverse of S and proposed a test based on asymptotic normality under H 0 of this modiﬁed T 2 statistic with appropriate location and scale transformation.”
On testing the equality of high dimensional mean vectors with unequal covariance matrices (2014, methodology): “Since then, more high dimensional tests have been proposed by Bai and Saranadasa (1996), Fujikoshi et al. (2004), Srivastava and Fujikoshi (2006), Srivastava (2007), Schott (2007), Srivastava and Du (2008), Srivastava (2009), Srivastava and Yanagihara (2010), Chen and Qin (2010) and Srivastava et…”
Statistical eigen-inference from large Wishart matrices (2007, methodology): “The issue of inverse covariance matrix estimation which Srivastava (2007) examines in the context of discriminant analysis is also related.”
Two-sample tests for high-dimension, strongly spiked eigenvalue models (2016, background): “In such situations, Dempster (1958, 1960) and Srivastava (2007) considered the test when π 1 and π 2 are Gaussian.”