Questions tagged [weighted-least-squares]

Question 1

I have a question that is related to weighted least-squares and operator norm. Assume we have a model $y(x) = a_1 \psi_1 + \dots + a_n \psi_n(x)$ and its noisy $N (>n)$meaurements $$ \{ (x_1, y(x_1)...

Question 2

I am trying to solve a standard least-squares problem of the form: $x = \text{argmin}|Ax-b|^2$, where $A$ has a non-trivial null space. I want the minimum 2-norm solution with the norm $\|x\|^2 = x^T ...

Question 3

I'm trying to generate a decent $[3,1]$ rational least squares polynomial approximation to $\arcsin(x)+\sqrt{1-x^2}$ and failing dismally :( The problem is that for this particular combination of $N,D$...

Question 4

The left pseudoinverse of $(A^TA)^{-1}A^T$ solves the problem of $\text{min} ||b-Ax||^2$. i.e. $x=(A^TA)^{-1}A^Tb$ is the solution to above problem. And there is a well-know property that if we add a ...

Question 5

If I have a $(X, Y)$ dataset and want to model $y = f(x, \beta)$. In that case for OLS, I would have $$e(x_i, \beta) = f(x_i, \beta) - y_i$$ Then obviously I would have $$SSE = \sum_{i}e(x_i, \beta)^2$...

Question 6

I've been tasked to calculate/forecast the weighted exposure of a financial product. I work with bunker prices and we have access to bunker future prices everyday. They look similar to this in an ...

Question 7

I am considering a weighted least square problem with data $X \in \mathbb{R}^{n \times p}$, (diagonal) weight matrix $W \in \mathbb{R}^{n \times n}$ and responses $y \in \mathbb{R}^n$, i.e. finding $$\...

Question 8

I have a problem I fail to research properly, so I hope you may at least push me in the right direction (or maybe even provide me an answer right away?). I know how linear regression works, that it ...

Question 9

I am currently working on a problem involving the minimization of the $\chi^2$ deviation between a model matrix ($C_{model}$) and a measured matrix ($C_{measured}$). by finding the best fit parameters ...

Question 10

Considering following linear model \begin{equation} y_t = X_t f_t + \varepsilon_t, \qquad t=1,\cdots, T \end{equation} where $y_t\in\Re^{300\times 1}$ and $X_t\in\Re^{300\times 60}$ are two given ...

Question 11

(also posted on CV, but I will try here too) I am trying to find out if what I am looking at is a known problem. I am considering the case of weighted least squares, and I am trying to find the ...

Question 12

I am trying to understand Jun Shao's proof of the asymptotic normality of weighted LSE in his book Mathematical Statistics. The theorem: Consider the model $X = Z\beta + \varepsilon$ with a full rank $...

Question 13

I was studying the weighted least squares algorithm and came across this formula for calculating the weighted result in terms of the original. Here $x_{LS}$ is the solution for $D=I$ I can't figure ...

Question 14

Let $x_1,...x_K \geq 0$ and $f$ be the piecewise-linear function given by $f(k)=x_k$ for every $1 \leq k \leq K$. Denote by $m$ the number of modes (i.e. local maxima) of $f$. Let's associate with ...

Question 15

We need to solve the following least square problem $$\min_x (Y-Ax)^TW(Y-Ax)$$ $$s.t. x^TA^TAx=1$$ $$c^Tx=0$$ in a closed form, where $Y \in \mathbb{R}^{n\times 1}$, $A \in \mathbb{R}^{n\times n}$, $W ...

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Questions tagged [weighted-least-squares]

Weighted least-squares that minimizes the operator norm

Solving minimum 2-norm least squares problem with a metric

Least squares rational approximation to $\arcsin x + \sqrt{1-x^2}$ in form $[3,1]$

Right pseudo-inverse and Generalized Least Squares

Weighted Least Squares versus ordinary least squares wiki page

Time Weighted Decay

Weighted Least Square with infinite weights

Linear regression for data points with given deviations?

Weighted Least squares with Multiple Unknowns and Iterations

Noise Covariance Estimation for Linear Regression (Seemingly Unrelated Regressions)

MSE of WLS estimator with biased measurements

Asymptotic Normality of Weighted LSE (Theorem 3.17, Jun Shao)

Weighted least squares formula

Best way to remove a local maxima from a piecewise linear function

Weighted least squares problem with a equal quadratic constraint

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