Questions tagged [weighted-least-squares]

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38 questions
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The derivative and extremum of a matrix function

$$f(W)=(Ax-b)^TW(Ax-b)=x^TA^TWAx-2b^TWAx+b^TWb$$ where $f(W)$ is a function of $W$, $A$ is a known matrix, $x$ and $b$ are vectors ($b$ is known). How to get $\frac{\partial f}{\partial W}$?
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How to scale a weighted variable for linear regression?

I would like to scale a variable such that after weighting it is scaled to mean zero and standard deviation one: $\sum_{i} w_{i} x_{i} = 0$ and $\sum_{i} w_{i} x_{i}^2 = 1$ where $w_{i}$ are ...
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Iteratively Weighted Least Squares and Hessian

The question is about stationary point of a least squares being identical to the stationary point of an error function as stated in: Computer Vision: Algorithms and Applications by Szelinski et al. p....
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Weighted rank 1 approximation to matrix

I want to solve the following problem: $$\arg\min_{u,v} \|W\odot(u v^\mathsf{T}-M)\|_\mathrm{F}$$ where $u$ and $v$ are $N\times 1$ vectors, $W$ and $M$ are $N\times N$ matrices, $\odot$ represents ...
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Statistics: Higher confidence, higher weight

So we have an experiment going on where a group of colleagues evaluate each other's skill levels, ranging from 1 to 5. We have $n$ colleagues, so in the end we should get $n^2$ evaluations. However, ...
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When can Levenberg-Marquardt fitting algorithm be used with least absolute residuals (LAR) method and not Bisquare method for residual minimization?

I am sorry for asking a trivial question but though I have found an answer in the following link, I would like to know some more insight on the situations when one residual minimizing method is used ...
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Alternatives to least square, overestimate?

Ok so I have a very simple linear system of equations with three unknowns and eight equations. Is there anyone that can tell me if there is a method or some way to find a solution which overestimates ...
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Weighted least squares estimator for a non-zero intercept regression

If I have the following regression model with intercept $\alpha$ $$y=X\beta + \alpha + \epsilon$$ Is the Weighted Least Squares (WLS) estimator for $\beta$ the same as in the zero-intercept ...