# Questions tagged [weighted-least-squares]

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38 questions
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### Weighted Least Squares and the unreal effect on the a posteriori MSE estimator

I expose the initial situacion and the questions are derived afterwards. Thanks a lot in advance, I hope the question is not too simple for this community. When solving normal or weighted least ...
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### Baseball: How are data sets with differing number of occurrences compared?

I have two data sets, each showing batting statistics for batters hitting against a specific pitcher. These tables show lifetime batting statistics of batters hitting against pitchers, therefore the ...
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### Weighted Least Squares - Categorical Data vs. Numerical Data

Over on Stackoverflow, I am trying calculate the Weighted Least Squares (WLS) of a data set in a python library called Numpy as compared to using a library called Statsmodels. However, I noticed ...
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### Minimizing a multivariable function with different vector length?

Assume that I want to minimize a function to a measured vector. $$V_{min} = \sum_{n = 0, k = 0}^{N, K}{|T_n - f(t_n, p_n, r_k)|}$$ Where $T_n, t_n, p_n$ has the same vector length $N$, but not $r_k$ ...
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The normal equation for weighted linear regression looks like this: $$J(\theta) = (X\theta - y)^TW(X\theta - y),$$ where $X\in\Re^{m\times n}$, $\theta\in\Re^{n\times n}$, $y\in\Re^{m\times 1}$, $W\... 2answers 264 views ### Weighted least squares with nuclear norm minimization Nuclear norm minimization is very popularization and formulation is least squares term with nuclear norm term as following, $$\min\limits_{X} \frac{1}{2}\|X_{3\times3}-Y_{3\times3}\|_F^2+\lambda\|X_{... 1answer 244 views ### Understanding Galerkin method of weighted residuals I have a puzzlement regarding the Galerkin method of weighted residuals. The following is taken from the book A Finite Element Primer for Beginners, from chapter 1.1. If I have a one dimensional ... 2answers 45 views ### Is there a least squares estimator for correlated, non-constant variance errors? For OLS we have \hat{\beta} = (X^TX)^{-1}X^Ty, For non-constant variance we have \hat{\beta} = (X^TWX)^{-1}X^TWy, but what if we have, for example Y = X\beta + \epsilon where \epsilon \sim N(... 1answer 272 views ### Weighted Least Squares Without Intercept I am studying the WLS model for y=\beta x+\epsilon, where \beta and x are vectors and \epsilon is the error term. This is a multiple regression model without an intercept. How would I find the ... 1answer 46 views ### polynomial least squares derivation: normal equations Suppose we have the problem$$ \min_{q \in \mathcal{P}_n} \|f - q\|_{L^2(w)}^2 $$where \mathcal{P}_n is the space of polynomials of degree n, w is some weight function (measure with continuous ... 2answers 560 views ### Linear Fit when Data has Uncertainty I am attempting to find the slope and y-intercept (along with their uncertainty) from a set of data. In this case, I am graphing Gamma Energy (MeV) vs. Peak Centroid (Channel). Here is my data: Gamma ... 1answer 118 views ### Weighted Least Squares for Parabola Coefficients Estimation I am in trouble to find where I am making a mistake... I have to estimate the parameters a and b of the curve modeled by: y = a x^2 + bx I have to do that from K measures of the curve, each ... 1answer 27 views ### what is the meaning of weighting in mathematics? What is the mathematical meaning of weighted by a Gaussian for numbers or vectors or Weighting by bilinear and weighted vectors? Regards and thanks in advance! 0answers 28 views ### Assign automatic weightage for set of negative numbers I have set of negative numbers e.g. [-0.189, -3.55, -19.90, -0.0001] now I have to convert this set to percentage such that largest number will have highest ... 1answer 218 views ### Stuck in concavity proof of least squares cost as a function of weights This problem comes from Boyd & Vandenberghe Convex Optimization, example 3.9 in page 81. All derivations make sense for me except the last step which says:$$g(w)=b^TWb-b^TWA(A^TWA)^{-1}A^TWb ... 2answers 48 views ### How to apply weightings to least squares slope formula Im using this formula to find the slope of the regression line of given$x,y$samples using LS calculation :$a=\frac{(n\sum xy-\sum x\sum y)}{(n\sum x^2-(\sum x)^2)}$How do i change it to apply ... 2answers 67 views ### 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$\frac{\partial f}{\partial W}$? 0answers 81 views ### Solving the two-parameter generalized Eigenvalue problem Is there a solution for the problem: $$(A_0 + \alpha \ A_1 + \beta \ A_2 ) x = 0$$ where:$ A_0, A_1,$and$A_2 \in \mathbb{R}^{n\times n}$,$\alpha$and$\beta \in \mathbb{C}$, and$x \in \mathbb{...
Let $f_1, f_2$ be given polynomials of degree $k$ and we want to find a polynomial $f$ of degree $k+1$ that solves the following minimization problem on $[0,1]$: f=\operatorname*{argmin}_{\hat{f}\in ...