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Re: OT: finding the weights used in weighted least squares regression
From: |
Ben Abbott |
Subject: |
Re: OT: finding the weights used in weighted least squares regression |
Date: |
Wed, 27 Apr 2011 08:24:52 -0400 |
On Apr 27, 2011, at 1:19 AM, Kamaraju S Kusumanchi wrote:
> Ben Abbott wrote:
>>
>> If I understand what you'd like to do, I think the solution is ...
>>
>> W = (A*(A\b)-b) ./ (A*x-b)
>>
>
> No. This is not the solution. Consider the following example
>
> octave:10> n=5, m=2, W = diag(rand(n,1)), A = rand(n,m), b = rand(n,1), x =
> (W*A) \ (W*b), (A*(A\b)-b) ./ (A*x-b)
> n = 5
> m = 2
> W =
>
> 0.63718 0.00000 0.00000 0.00000 0.00000
> 0.00000 0.75466 0.00000 0.00000 0.00000
> 0.00000 0.00000 0.69982 0.00000 0.00000
> 0.00000 0.00000 0.00000 0.08992 0.00000
> 0.00000 0.00000 0.00000 0.00000 0.94621
>
> A =
>
> 0.833095 0.568790
> 0.792483 0.536521
> 0.702069 0.588282
> 0.036704 0.529085
> 0.238762 0.427252
>
> b =
>
> 0.86356
> 0.77943
> 0.77652
> 0.98000
> 0.49344
>
> x =
>
> 0.32941
> 0.97441
>
> ans =
>
> 2.07510
> -7.79993
> 2.55568
> 0.23533
> 112.87186
>
>
> Hence W is not same as (A*(A\b)-b) ./ (A*x-b) .
>
> thanks
> --
> Kamaraju S Kusumanchi
> http://malayamaarutham.blogspot.com/
Ok. I see my mistake now. Essentially you want to solve for W where ...
diag (W) * (A * x - b) = c
But you don't know "c". However, you do know that "c" are the least square
errors.
I don't see a direct solution. Would an iterative solution work?
I don't know how stable it would be but, is something like below acceptable?
err = @(u) x - (diag (u) * A) \ (diag (u) * b);
W = fsolve (err, ones (n, 1))
I expect the options for fsolve will need to be added to get an accurate result.
Ben
- OT: finding the weights used in weighted least squares regression, Kamaraju S Kusumanchi, 2011/04/26
- Re: OT: finding the weights used in weighted least squares regression, Ben Abbott, 2011/04/26
- Re: OT: finding the weights used in weighted least squares regression, Kamaraju S Kusumanchi, 2011/04/27
- Re: OT: finding the weights used in weighted least squares regression, James Sherman Jr., 2011/04/27
- Re: OT: finding the weights used in weighted least squares regression, Kamaraju S Kusumanchi, 2011/04/27
- Re: OT: finding the weights used in weighted least squares regression,
Ben Abbott <=
- Re: OT: finding the weights used in weighted least squares regression, Kamaraju S Kusumanchi, 2011/04/27
- Re: OT: finding the weights used in weighted least squares regression, Ben Abbott, 2011/04/27
- Re: OT: finding the weights used in weighted least squares regression, Kamaraju S Kusumanchi, 2011/04/27
- Re: OT: finding the weights used in weighted least squares regression, Mike Miller, 2011/04/28