# Applications in Statistics

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## 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, *XT**X*, 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## Preview

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