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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

1625.0. "Computing the t statistic for regression" by EPIK::FINNERTY (The bug stops here) Wed Jun 10 1992 12:08

    
    For computing a t-statistic I need to compute the main diagonal of the
    inverse of a matrix.
    
    If the matrix is first converted to LU form, the inverse, as I
    understand it, can be calculated on each half of the matrix seperately;
    the equation for the main diagonal turns out to be simply 1/Aii in this
    case.
    
    So, if I only need the main diagonal to compute the t statistic, and
    the main diagonal is already available from U (even without inclusion
    of the Gaussian multipliers for L), can't I just take 1/Aii on the main
    diagonal of the 'solved' matrix to compute the t statistic without
    computing the inverse for the entire matrix explicitly?
    
       /Jim

T.R	Title	User	Personal Name	Date	Lines
1625.1	I worry a bit about that	SGOUTL::BELDIN_R	All's well that ends	`Wed Jun 10 1992 15:04`	8
	I'll take your word that you only need to compute the main diagonal because I don't know your model, and if so, your conjecture is correct. What worries me is that most multivariate models compensate for correlations between the variables which depend on the off-diagonal elements. You could be making an invisible assumption of independence or lack of correlation. Dick
1625.2		EPIK::FINNERTY	The bug stops here	`Thu Jun 11 1992 09:05`	14
	...if there's a better/easier way of computing the t statistic, I'd be glad to know of it. The definition of the t statistic that I have uses the elements on the main diagonal of the inverse (only). the information I'm working from does, indeed, make the assumption that the model is linear in the parameters (though there may be a nonlinear relationship between the variables). what is the recommended way to, as you say, compensate for correlations between the variables? /Jim
1625.3	more on multivariate t	MOCA::BELDIN_R	All's well that ends	`Thu Jun 11 1992 13:45`	15
	You won't like this 'cause its not easier. 'Better' depends on your trust in the uncorrelated variable assumption. A multivariate T� statistic (due to Mahalanobis) is analogous to the univariate one, but uses the inverse of the covariance matrix instread of dividing by the std deviation. Soooo... T� = k(x-�)'U(x-�) where U�S = I and S is the covariance matrix and x and � are column vectors and k is a constant which depends on the sample size and the number of components in x. �, of course, is determined by your hypothesis. I'll look up a reference tonight. Dick
1625.4	Perhaps he should write under the pseudonym "Teacher"	VMSDEV::HALLYB	Fish have no concept of fire.	`Thu Jun 11 1992 15:05`	9
	> A multivariate T� statistic (due to Mahalanobis) is analogous to the > univariate one, but uses the inverse of the covariance matrix instread > of dividing by the std deviation. Soooo... In certain lands Mahalanobis would be beheaded for introducing this idea. :-) John