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)
Famous quotes containing the words examples of, examples and/or forms:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)
“It is given to few to add the store of knowledge, to strike new springs of thought, or to shape new forms of beauty. But so sure as it is that men live not by bread, but by ideas, so sure is it that the future of the world lies in the hands of those who are able to carry the interpretation of nature a step further than their predecessors.”
—Thomas Henry Huxley (1825–95)