RE: cov. matrix of a stabilized wlsq fit

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#3540

From: Bill Venables
Date: Wed, 12 Feb 1992 22:51

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You write
>
> 	   In general,let your estimator be
>
> 	   x = Gy , where matrix G does not involve y.  Then
> the covariance matrix of your estimator is
> 	   Cov(x) = GCG'.
>
> In your second case, the covariance matrix is
>
> 	   Cov(x) = inv(A'*W*A+alpha*E)*A'*inv(A'*W*A+alpha*E)'

Oops!  There's a few bits missing here (in fact the matrix sizes don't
match)

I think you mean

> 	   Cov(x) = inv(A'*W*A+alpha*E)*A'*C*A*inv(A'*W*A+alpha*E)'
                                          ^^^^
However this is only the case if alpha is specified in advance and not
estimated as a parameter.  The original question was somewhat obscure about
which was the case.

--
Bill Venables, Dept. of Statistics, | Email: venables@stats.adelaide.edu.au
Univ. of Adelaide, South Australia. | Tel: +61 8 228 5412  Fax: ...232 5670

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From:         Bill Venables <wvenable@STATS.ADELAIDE.EDU.AU>
Subject:      RE: cov. matrix of a stabilized wlsq fit
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