Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [determinant]

The tag has no usage guidance.

0
votes
0answers
10 views

is there a relationship between the determinant and the convolution

A long time ago, perhaps 13 or 16 years, I took a course called linear algebra. It has been a little while,so in parts that I don't use as much I was rusty. I possibly incorrectly remember having to ...
0
votes
0answers
29 views

Understanding MCD

I have recently stumpled upon the robust MCD (Minimal Covariance Determinant) Estimator. If I have $n$ datapoints of dimension $p$. Let`s say we want to obtain a robust estimate for the Covariance ...
0
votes
0answers
32 views

Name of a second order statistical quantity similar to generalized variance

I am looking for the name of a statistical quantity similar to generalized variance in a 2 dimensional space. Specifically, I define generalized variance as $\epsilon_{a,b}^2 = \left|\begin{matrix}\...
3
votes
1answer
150 views

Why does the determinant of the Hessian grow with n?

Context: I'm trying to understand BIC on a deeper level. I'm using BIC for model/structure selection for Bayesian networks. I'm confused because BIC is an approximation to the likelihood of a model, ...
4
votes
1answer
113 views

How to model for independent determinants in several groups based on follow-up time

I want to answer the research question which determinants are associated with long-term survival after a myocardial infarction (MI) in a prospective patient cohort study. More precisely: I want to ...
6
votes
1answer
2k views

Do the Determinants of Covariance and Correlation Matrices and/or Their Inverses Have Useful Interpretations?

While learning to calculate covariance and correlation matrices and their inverses in VB and T-SQL a few years ago, I learned that the various entries have interesting properties that can make them ...
2
votes
0answers
980 views

Multicollinearity (or not) in exploratory factor analysis

I’m performing an exploratory factor analysis with 28 items, n = 300. I’m confused whether I have a multicollinearity problem or not, and if so whether/how I go about choosing items to remove from the ...
3
votes
0answers
117 views

Algebraic derivation of canonical correlations

In a paper from 1936, Harold Hotelling (access on JSTOR) defined the concepts of canonical correlations and canonical variates for two sets of variates. In pages 327 and 328, he precisely derives ...
1
vote
0answers
188 views

Log Expectation of Inflated Determinant of Wishart Distribution

Let $\Lambda \sim \mathcal W(\nu, \Psi)$, i.e., following a $n \times n$ dimensional Wishart distribution with mean $\nu \Psi$ and degrees of freedom $\nu$. The expectation of the log determinant of $\...
3
votes
1answer
120 views

Determinant of a block matrix with sparse elements

I have a positive definite symmetric matrix that looks like $$\pmatrix{A & 0 & 0 & E \\ 0 & B & 0 & F \\ 0 & 0 & C & G \\ E^\prime & F^\prime & G^\prime &...
0
votes
1answer
169 views

How to get the determinant of a covariance matrix from its diagonal elements

I am trying to implement a speaker recognition system in MATLAB. I am using Gaussian Mixture Models (GMM) for speaker modelling and maximizing the posterior probabilities for classification. The ...
2
votes
0answers
88 views

Stability of VAR$(p)$: Prove $\det(I_{Kp}-\tilde{A}z)=\det(I_k-A_1z-\ldots-A_pz^p)$

Given we have a VAR$(p)$ process written in the companion form $$\tilde{y}=\tilde{v}+\tilde{A}\tilde{y}_{t-1}+\tilde{u}_t$$ where $$\tilde{A}=\left(\begin{array}{ccccc} A_1& A_2 & \ldots &...
7
votes
1answer
633 views

How is the determinant of $(X'X)$ related to variance?

I'm working on a problem (and actually have the answer) but I don't know why this is the answer, can someone explain this equality?. It has to do with the the determinant of the partitioned matrix $(X'...
1
vote
1answer
35 views

What's special about (x'x-x'Proj(w)x)?

I'm working on my homework and I keep seeing something like $$(x'x-x'W(W'W)^{-1}W'x)$$ I know that $W(W'W)^{-1}W'$ is the projection matrix, but what is so special about subtracting those two inner ...
1
vote
1answer
42 views

Column1 = Temp_F and Column2 = Temp_C — are these linearly dependent?

If $X$ is a matrix of size $m$ x $2$, where the first column is a range of Celsius values and the second column is their corresponding Fahrenheit values, would the columns be considered linearly ...
3
votes
1answer
112 views

Meaning of determinant of matrix of impulse-response functions in a VAR

Suppose there is a structural VAR model, such as: $A y_{t} = B y_{t-1} + \varepsilon_{t}$, where $\varepsilon_{t} \sim N(0, I_{n})$; then the matrix representing the contemporaneous impulse-response ...
1
vote
1answer
100 views

Sampling from an (almost) multivariate normal over matrices

Consider $n$ points in the euclidean plane, $p_i = (x_i,y_i)_{1\leq i \leq n}$. Now consider a $2 \times 2$ matrix $M = \left(\begin{array}{cc}a & b\\c& d\end{array}\right)$ a vector $r = \...
0
votes
2answers
868 views

Applying inferential statistics for census data

Let's assume I have a census data of a population which I would like to study and it has variables such as age, gender, sex, occupation etc and the dependent variable which is community participation ...
8
votes
1answer
2k views

How to generate uniformly random orthogonal matrices of positive determinant?

I've got probably a silly question about which, I must confess, I'm confused. Imagine repeated generating of uniformly distributed random orthogonal (orthonormal) matrix of some size $p$. Sometimes ...
9
votes
2answers
1k views

Fisher information matrix determinant for an overparameterized model

Consider a Bernoulli random variable $X\in\{0,1\}$ with parameter $\theta$ (probability of success). The likelihood function and Fisher information (a $1 \times 1$ matrix) are: $$ \begin{align} \...
1
vote
1answer
318 views

Determinant of the covariance matrix in a normal distribution

Suppose a $p \times 1$ vector $x \sim N_p(\boldsymbol 0, \boldsymbol \Sigma_1)$. Now, There is another covariance matrix $\boldsymbol \Sigma_2$. We know that $|\boldsymbol \Sigma_2| < |\boldsymbol \...
8
votes
1answer
219 views

Why people often optimize the determinant of $(X'\Sigma X)^{-1}$

Say I have a random vector $Y\sim N(X\beta,\Sigma)$ and $\Sigma\neq\sigma^2 I$. That is, the elements of $Y$ (given $X\beta$) are correlated. The natural estimator of $\beta$ is $(X'\Sigma^{-1}X)^{-1}...
1
vote
1answer
2k views

What does Determinant of Covariance Matrix give?

I am representing my 3d data in covariance matrix. I just want to know what the determinant of a covariance matrix gives. If the determinant is positive, zero, negative, high positive, high negative, ...
0
votes
1answer
601 views

How to calculate Eigenvalue without using eign() function with R? [closed]

I understand how to calculate EIGN by hand but when I try to write code without function EIGN(), I did not have a clue. To calculate Eigenvalue is to count all the possible c in ...
6
votes
2answers
8k views

Why do we use the determinant of the covariance matrix when using the multivariate normal?

I am not well versed in statistics. I wanted to know why we use the determinant of the covariance matrix instead of having the covariance matrix itself when writing down the multivariate normal ...
34
votes
3answers
35k views

Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to be positive semi-definite?

I have been researching the meaning of positive semi-definite property of correlation or covariance matrices. I am looking for any information on Definition of positive semi-definiteness; Its ...
4
votes
1answer
8k views

Factor analysis: What to do when determinant is almost zero and when KMO for a variable is low?

I'm conducting a factor analysis on 40 interval-level variables, and have two immediate concerns: The determinant is 6.608E-006, which is much lower than the cut-...
2
votes
1answer
385 views

MLE estimation of spatial effects radius

I am trying to identify the maximum likelihood estimates in an SDM model (a hedonic home price model, with observations being 5,000 individual homes), $$y=\rho W y + X\beta + WX\lambda + \epsilon$$ ...