0
votes
0answers
20 views

Is there a bound on largest eigenvalue for covariance matrix of discrete random variable?

I have a random variable $Z=(Z_1,\ldots,Z_p)$. Each component can take values in {-1,0,1}. Is there a way to bound the largest eigenvalue of Cov(Z)? Actually, I have a latent multinormal variable ...
0
votes
0answers
24 views

steps in factor analysis in matlab

i know basically how to express PCA mathematicaly,but i would like to know steps that should be used for factor analysis,let us consider some matrix,for instance ...
0
votes
0answers
18 views

PCA - How to calculate the scores

I'm currently learning Principle component analysis and I have, so far calculated the Eigen values and vectors. Assume that I have the following: $$ E = \begin{pmatrix} 1 & 2\\ 3& 4 ...
0
votes
0answers
24 views

MSE of weighted PCA estimator

I need to calculate the variance of this estimator which is a generalisation of the OLS estimator: OLS: $Y=X\beta+e$ where Y is n*1 vector of responses X is n*p pbserved matrix of regressor ...
0
votes
0answers
55 views

Bias in Principal Components Regression

Assume we have the well known OLS model $Y=X\beta+e$ where Y is n*1 vector of responses X is n*p pbserved matrix of regressor variables $\beta$ is a p*1 vector of unknown parameters e is a n*1 ...
2
votes
1answer
26 views

Bug in deriving PCA

Ok, I feel dumb. From what follows it looks like there is a bug in my reasoning. There are $N$ datapoints $\boldsymbol{x}_n$. $\hat{\boldsymbol{u}}$ will be the direction of my principal component, ...
3
votes
1answer
283 views

Covariance- v. correlation-matrix based PCA

In principal component analysis (PCA), one can choose either the covariance matrix or the correlation matrix to find the components. These give different results because, I suspect, the eigenvectors ...
5
votes
2answers
615 views

Eigenvalue decomposition of block covariance matrix for Canonical Correlation Analysis (CCA)

Edited: My question is related to a tutorial I was reading. The covariance matrix is a block matrix where $C_{xx}$ and $C_{yy}$ are within-set covariance matrices and $C_{xy} = C_{yx}^T$ are ...
1
vote
2answers
373 views

What relationship between matrices (Multivariate Statistics)

I am working with sampling of multivariate normally distributed numbers. I have a very fundamental question regarding the eigendecomposition of the $k \times k$ covariance matrix $\Sigma = ...
6
votes
1answer
555 views

Symmetric matrix decomposition with orthonormal basis of non-eigenvectors

I like to understand the following transformation found in documentation for deriving Kalman filter. Abstract Formulation: Given 2 symmetric matrices $A$ ,$B$ $\in$ $\mathbb R^{3,3}$ with $A \ne B$ ...