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)
“Of the three forms of pride, that is to say pride proper, vanity, and conceit, vanity is by far the most harmless, and conceit by far the most dangerous. The meaning of vanity is to think too much of our bodily advantages, whether real or unreal, over others; while the meaning of conceit is to believe we are cleverer, wiser, grander, and more important than we really are.”
—John Cowper Powys (1872–1963)