Questions tagged [qr-decomposition]

Question 1

Here is my attempt to show that INDSCAL as a special case of CANDELINC. I am using the following paper as my reference for definitions. Kolda, Tamara G., and Brett W. Bader. "Tensor ...

Question 2

I'm starting to more routinely mean-center and QR-rotate design matrices $X$ when doing maximum likelihood estimation (MLE) or Bayesian posterior sampling. This helps with convergence and quickens ...

Question 3

I am trying to understand the code from pybasicbayes, which defines the following function to sample from an inverse Wishart: ...

Question 4

Assuming $\mathbf x_1$ and $\mathbf x_2$ are eigenvectors of matrix $\mathbf A \in \mathbb{R}^{2\times 2}$, there is $$\left(\mathbf I-\mathbf x_1\mathbf x_1^\top\right)\mathbf A\left(\mathbf I-\...

Question 5

I'm using rstanarm to estimate random slopes for second-order polynomial coefficients. My model has the basic form: ...

Question 6

I am a recent enthusiast into linear modelling and working on a function in R that implements common calculations from lm in R, to better understand how it works. ...

Question 7

I'm doing PCA in a covariance matrix where each column and row represents tenors of the yield curve. I have coded the Jacobi rotation method and I also have a QR algorithm based on numpy.linalg.qr in ...

Question 8

I apologize if this is the wrong place for this question; there are a number of potential points of failure each of which suggest either Math StackExchange or StackOverflow or here, but since the ...

Question 9

I am struggling to find a reference for this: In terms of big Oh notation does anyone know of any expressions for the computational time taken by commonly used algorithms for QR decompositions?

Question 10

I know that the calculation of parameter values of a standard OLS can be made more efficient using a QR decomposition; i.e. if $X=QR$ and we are using the model $Y=X\beta+\epsilon$; Then it is true ...

Question 11

Considering design matrix $X \in \mathbb{R}^{n\times p}$ $(n>p)$ and response $y\in \mathbb{R}^{n}$. The sandwich estimator can be calculated directly using $$(X^TX)^{-1}X^T diag(r^2) X (X^TX)^{-...

Question 12

I am using a linear regression, yet the only output I need is the Sum of Squared Residuals (SSR), I don't care about the coefficients. (Context is a non-linear LS, which is linear given an extra ...

Question 13

I am trying to understand if the ordering of columns matters in QR decompsoition. In general it seems that column ordering won't matter. I guess for SVD or any matrix factorization the way columns ...

Question 14

Suppose $Q_{1}$ is an $n$ x $p $ matrix (derived from the QR Decomposition of X) whose columns provide an orthonormal basis for the subspace ${\chi}$ of $\mathbb{R}^{n}$ spanned by the columns of an $...

Question 15

Here is the source code of R poly function (boundary checking are removed). Why we can use QR to build polynomial expansion, ...

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Questions tagged [qr-decomposition]

INDSCAL as a special case of CANDELINC

Transforming Hessian to original parameters after centering and QR-transforming X

How to sample efficiently from an inverse Wishart distribution?

QR Iteration convergence

Quadratic regression with orthogonal polynomials vs. raw polynomials with QR decomposition

Getting least squares calculations from QR decomposition

Order of eigenvalues when using different methods

Why is my QR decomposition updating code numerically off?

QR decomposition computational efficiency

Generalised least squares using QR decomposition

Calculating sandwich estimator

Fast way to obtain SSR (Sum of Squares residuals) from QR in least square model?

Does Column ordering matter in QR decomposition?

Relationship between X and its projection matrix [closed]

Orthogonal polynomial expansion and QR decomposition

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