Abstract
This chapter explains how inequalities play an important role in statistics. Many results, such as the Cramer–Rao inequality, which provides the lower bound of the variance of any estimate of a parameter, are extremely important in theoretical statistics. Some of these inequalities are derived from classical inequalities in mathematics. Inequalities can often be derived from the application of optimization methods. The most universal weapon for the discovery and proof of inequalities is the general theory of maxima and minima of functions of any number of variables. In multivariate statistical problems and many other similar situations, matrices are involved, for example, in quadratic forms. Some multivariate statistical analysis involves matrices also.
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