Quadratic Form (statistics) - Examples of Quadratic Forms

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)

    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)

    Pervading nationalism imposes its dominion on man today in many different forms and with an aggressiveness that spares no one.... The challenge that is already with us is the temptation to accept as true freedom what in reality is only a new form of slavery.
    Pope John Paul II (b. 1920)