The matrix-inverse tag has no wiki summary.
2
votes
2answers
399 views
Numerical Instability of calculating inverse covariance matrix
I have a 65 samples of 21-dimensional data (pasted here) and I am constructing the covariance matrix from it. When computed in C++ I get the covariance matrix pasted here. And when computed in matlab ...
0
votes
1answer
110 views
Singular matrix: eigenvalues perturbation vs Moore-Penrose generalized inverse
We often face singular matrices in practice: OLS with singular (X'X), GMM with singular weighting matrix, singular matrix in Wald statistics. I'm wondering how can we overcome this issue. I've seen ...
0
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0answers
28 views
Ensuring the covariace matrix is invertible [duplicate]
I know that when constructing a sample covariance matrix from d-dimension vectors we need at least $d+1$ samples. But are there any other constraints to ensure that the matrix will be invertible?
3
votes
2answers
265 views
Ways to measure distance from multivariate Gaussian (Mahalanobis distance)
I have a cluster of p-dimensional points and given a new p-dimensional point $x$ I want to determine whether or not it is likely to belong to this cluster.
The cluster is made up of $n$ ...
2
votes
1answer
292 views
What to do when sample covariance matrix is not invertible?
I am working on some clustering techniques, where for a given cluster of d-dimension vectors I assume a multivariate normal distribution and calculate the sample d-dimensional mean vector and the ...
2
votes
1answer
65 views
How to interpret the sum of the elements of an inverse covariance matrix?
In the derivation of global minimum variance portfolio, we get The $(Σ^{-1}1) /(1'Σ^{-1}1)$. What's the meaning of $1'Σ^{-1}1$ and $Σ^{-1}1$. $Σ$ is a covariance matrix of assets returns.
0
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0answers
75 views
How to derive the partial correlations interpretation of inverse covariance matrix?
How to derive the partial correlations interpretation of inverse covariance matrix by using the Schur complement to get a formula for the entries of the inverse covariance matrix in terms of the ...
3
votes
1answer
77 views
Question about inverse in a two-step estimator as a joint GMM-estimators approach
I'm reading Newey & McFadden - Large sample estimation and hypothesis testing (in the Handbook of Econometrics, Volume 4, 1994, page 2178).
My model which I'm interested in has some former ...
2
votes
1answer
127 views
How to get conditional variance from Schur complement?
Suppose you have vectors X and Y with covariance matrix
$V = \left( \begin{array}{cc}
A & B \\
B^T & C \end{array} \right)$. This Wikipedia article says that $Var(X | Y) = A - BC^{-1}B^T$, ...
2
votes
1answer
94 views
Correlation and Hotelling test
To find a Hotelling $T^2$ score it is necessary to calculate the covariance matrix and then invert it.
Now, when the test is a two-sample $T^2$ test, the covariance matrix is a pooled matrix. When ...
0
votes
1answer
101 views
Pseudo Inverse Instead of Inverse with LDA?
I have implemented the LDA algorithm. However when I had to get the inverse of a matrix Matlab threw an error and I had to use pinv (pseudo inverse) instead of inverse. Did I do something wrong or is ...
2
votes
0answers
332 views
Geometric intuition for why an outer product of two vectors makes a correlation matrix? [closed]
I understand that the outer product of two vectors, say representing two detrended time series, can represent a cross-correlation (well covariance) matrix.
I also know that the inverse of a ...
0
votes
1answer
221 views
matlab gmdistribution.fit 'Regularize' - what regularization method?
I am wondering what is behind matlab 'Regularize' option for method gmdistribution.fit. If it is simply adding a 'little' value to diagonal elements of covariance matrix, so as to make covariance ...
1
vote
0answers
85 views
Estimation accuracy of precision matrix
I have a couple of questions related to estimation of high-dimensional precision matrix (inverse of the covariance matrix) in the case where p is close to 100 and n < p. As a measure of estimation ...
3
votes
1answer
176 views
Moore-Penrose generalized determinant
Is there a function in R to calculate the generalized determinant of a singular matrix? (similar to the ginv() used to compute the generalized inverse)
5
votes
3answers
429 views
To use Discrete Fourier Transform to invert a covariance matrix
I am working on a problem that its difficult part is to invert a covariance matrix (in R). I could not use usual approches like SVD and Chol. Then, I decided to use a Discrete Fourier Transform (DFT) ...
0
votes
1answer
773 views
Problem with singular covariance matrices when doing gaussian process regression
I'm working with gaussian process regression. Currently I start testing differnt covariance functions and compositions to see what type of data they could describe best. I made an own implementation ...
0
votes
2answers
495 views
Gaussian Process covariance matrix gets zero determinant
i have a gaussian process regression implementation and developed some example data to test the capabilities of those methods. In the posterior calculation one gets the covariance matrix K. For some ...
3
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4answers
1k views
Testing for linear dependence among the columns of a matrix
I have a correlation matrix of security returns whose determinant is zero. (This is a bit surprising since the sample correlation matrix and the corresponding covariance matrix should theoretically be ...
7
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1answer
2k views
Efficient calculation of matrix inverse in R
I need to calculate matrix inverse and have been using solve function. While it works well on small matrices, solve tends to be ...
9
votes
1answer
232 views
Fast computation/estimation of a low-rank linear system
Linear systems of equations are pervasive in computational statistics. One special system I have encountered (e.g., in factor analysis) is the system
$$Ax=b$$
where $$A=D+ B \Omega B^T$$
Here $D$ is ...
1
vote
1answer
213 views
Solving a regression problem
I wanted to solve such a regression problem:
$$Y = Xb + e$$
where $X$ is a $m$ by $n$ matrix, resulting in: b = (X'X)-1X'Y as a solution. Since $n$ is quite large (2400), I can't use the ...
6
votes
3answers
287 views
Computing $(X^TX)^{-1}X^Ty$ in OLS
Let $A\in\mathbb{R}^{n \times n}$ be a dense symmetric positive-definite matrix (the $X^TX$ from here) and $b$ a vector in $\mathbb{R}^n$.
I need to compute $A^{-1}b$.
Two questions:
Could you ...
