Examples of Quadratic Forms
In the setting where one has a set of observations and an operator matrix, then the residual sum of squares can be written as a quadratic form in :
For procedures where the matrix is symmetric and idempotent, and the errors are Gaussian with covariance matrix, has a chi-squared distribution with degrees of freedom and noncentrality parameter, where
may be found by matching the first two central moments of a noncentral chi-squared random variable to the expressions given in the first two sections. If estimates with no bias, then the noncentrality is zero and follows a central chi-squared distribution.
Read more about this topic: Quadratic Form (statistics)
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