# 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
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