Max-stable models for multivariate extremes

Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models for univariate and multivariate extremes. A comprehensive account is given of the various ways in which max-stable models are described. Furthermore, a construction device is proposed for generating parametric families of max-stable distributions. Although the device is not new, its role as a model generator seems not yet to have been fully exploited.Comment: Invited paper for RevStat Statistical Journal. 22 pages, 3 figure

Closed-form expression for finite predictor coefficients of multivariate ARMA processes

We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed sizes independent of the number of observations. The significance of the expression is that it provides us with a linear-time algorithm to compute the finite predictor coefficients. In the proof of the expression, a correspondence result between two relevant matrix-valued outer functions plays a key role. We apply the expression to determine the asymptotic behavior of a sum that appears in the autoregressive model fitting and the autoregressive sieve bootstrap. The results are new even for univariate ARMA processes.Comment: Journal of Multivariate Analysis, to appea

Admissible estimator of the eigenvalues of the variance-covariance matrix for multivariate normal distributions

An admissible estimator of the eigenvalues of the variance-covariance matrix is given for multivariate normal distributions with respect to the scale-invariant squared error loss.ArticleJOURNAL OF MULTIVARIATE ANALYSIS. 102(4): 801-815(2011)journal articl

Latent Structures based-Multivariate Statistical Process Control: a paradigm shift

The basic fundamentals of statistical process control (SPC) were proposed by Walter Shewhart for data-starved production environments typical in the 1920s and 1930s. In the 21st century, the traditional scarcity of data has given way to a data-rich environment typical of highly automated and computerized modern processes. These data often exhibit high correlation, rank deficiency, low signal-to-noise ratio, multistage and multiway structures, and missing values. Conventional univariate and multivariate SPC techniques are not suitable in these environments. This article discusses the paradigm shift to which those working in the quality improvement field should pay keen attention. We advocate the use of latent structure based multivariate statistical process control methods as efficient quality improvement tools in these massive data contexts. 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