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Applications in Statistics

  • James E. Gentle
Chapter
Part of the Statistics and Computing book series (SCO)

Abstract

One of the most common structures for statistical datasets is a two-dimensional array. A matrix is often a convenient object for representing numeric data structured this way; the variables on the dataset generally correspond to the columns, and the observations correspond to the rows. If the data are in the matrix X, a useful statistic is the sums of squares and cross-products matrix, XTX, or the “ adjusted” squares and cross-products matrix, where X a is the matrix formed by subtracting from each element of X the mean of the column containing that element. The matrix where n is the number of observations (the number of rows in X), is the sample variance-covariance matrix. This matrix is nonnegative definite (see Exercise 6.1a, page 176). Estimates of the variance-covariance matrix or the correlation matrix of the underlying distribution may not be positive definite, however, and in Exercise 6.1d we describe a possible way of adjusting a matrix to be positive definite.

Keywords

Normal Equation Full Rank Markov Chain Model Linear Equality Constraint Ridge Regression Estimator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • James E. Gentle
    • 1
  1. 1.Institute for Computational Sciences and InformaticsGeorge Mason UniversityFairfaxUSA

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