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If we have the estimator $(X^{T}WX)^{-1}X^{T}Wy$ where the diagonal of W contains the inverted weights, what is the fastest/most efficient way to solve it?

I know with OLS, the estimator is typically solved using QR decomposition, but does this method work just as well with WLS?

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If $W$ is diagonal as you say, then there should be a simple matter to scale each observation (both regressors and response) with $w_{ii}^{1/2}$ and then use the regular QR decomposition.

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