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Forum index » Science and Technology » Math » Probability » Prediction
parameters estimation
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xanthos george
science forum beginner


Joined: 22 Aug 2005
Posts: 4

PostPosted: Tue May 23, 2006 3:07 am    Post subject: parameters estimation Reply with quote
for i=1,2,3,...n j=1,2,3,...m
and e(i,j) ~Normal(0, ó^2/w(i,j))

y(i,j) = a+b(i)+ã(j)+e(i,j)

if y(i,j) values are known

How can i estimate a, b(i) and ã(j) parameters ?

Thanks alot
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Ray Koopman
science forum Guru Wannabe


Joined: 25 Mar 2005
Posts: 216

PostPosted: Tue May 23, 2006 4:04 am    Post subject: Re: parameters estimation Reply with quote
xanthos george wrote:
Quote:
for i=1,2,3,...n j=1,2,3,...m
and e(i,j) ~Normal(0, ó^2/w(i,j))

y(i,j) = a+b(i)+ã(j)+e(i,j)

if y(i,j) values are known

How can i estimate a, b(i) and ã(j) parameters ?

Thanks alot

Use weighted least squares, weighting each y by the corresponding w.
But note that you need some sort of constraints on b and ã,
such as setting one member of each set to zero,
or forcing each set to sum to zero.
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xanthos george
science forum beginner


Joined: 22 Aug 2005
Posts: 4

PostPosted: Tue May 23, 2006 5:20 am    Post subject: Re: parameters estimation Reply with quote
Thanks very much mr R Koopmam
Do you know whrere i can find any solved example ?

? "Ray Koopman" <koopman@sfu.ca> ?????? ??? ??????
news:1148357095.169498.185910@i39g2000cwa.googlegroups.com...

xanthos george wrote:
Quote:
for i=1,2,3,...n j=1,2,3,...m
and e(i,j) ~Normal(0, ó^2/w(i,j))

y(i,j) = a+b(i)+ã(j)+e(i,j)

if y(i,j) values are known

How can i estimate a, b(i) and ã(j) parameters ?

Thanks alot

Use weighted least squares, weighting each y by the corresponding w.
But note that you need some sort of constraints on b and ã,
such as setting one member of each set to zero,
or forcing each set to sum to zero.
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Ray Koopman
science forum Guru Wannabe


Joined: 25 Mar 2005
Posts: 216

PostPosted: Tue May 23, 2006 5:48 pm    Post subject: Re: parameters estimation Reply with quote
xanthos george wrote:
Quote:
Thanks very much mr R Koopmam
Do you know whrere i can find any solved example ?

Read up on analysis of variance (anova). What you're describing is
a two-way anova model for the cell means, with w(i,j) playing the
role of the sample size in cell (i,j). You will probably have to use
the general linear model (GLM) approach to estimating the parameters.
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Google
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