Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 2, pp. 232-264

AGGREAGATED MULTIVARIATE MEASURES PERFORMED UNDER CHANGING CIRCUMSTANCES

By

JEAN-DANIEL ROLLE, University of Geneva, Geneva

SUMMARY. We propose and analyze a model built to treat data presenting the following characteristics: 1. they appear in an aggregated form 2. the aggregated terms may be considered as multivariate measures performed by instruments of random accuracy, or by the same instrument in changing conditions 3. the data have a p-way classification. This type of data is encountered in several situations, including railroad or telephone demand studies or other network analyses. In the context of a regression model, we provide explicit estimators for the covariance matrix of the response, and discuss their characteristics and limitations. The estimators are obtained by optimization of functions of matrices. The model is applied to a set of real data. The interpretation of the results incidentally allows us to illustrate special features of the family of non-Gaussian compound normal distributions.

AMS (1991) subject classification.62H12.

Key words and phrases. Linear regression; compound normal distributions; quadratic and nonnegative estimation of the eigenvalues of a covariance matrix.

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