In mathematical terms, the principal components of the distribution of faces or the eigenvectors of the covariance matrix
of the set of face images, is sought by treating an image as a vector in a very high dimensional face space.
The fixed curve was modeled by second and third order polynomial regressions using 12 matrix structures of the random variance and covariance matrix
(G), maintaining the residual effects matrix (R) always equal to the VC.
The inverse of the asymptotic covariance matrix
In contrast, in blind channel estimation, the covariance matrix
of the received signal vectors is exploited to estimate the channel coefficients .
X] is the posteriori covariance matrix
of the state parameters; Q is the covariance matrix
of the processing noise; K is the gain matrix of the Kalman filter; H is the coefficient matrix of the observation equation; P is the observation weight matrix; R is the observation noise variance matrix, such that R = [P.
Then, the covariance matrix
of sample matrix is calculated by the following formula:
Investors who know their VaR limit, expected security returns, and the covariance matrix
of those asset returns, can plug those into closed form solutions for portfolio weights, portfolio expected returns, and portfolio standard deviation.
It is convenient to assume that the error term et is Gaussian with mean 0 and covariance matrix
Where Cov_mat in this equation is the estimation covariance matrix
after post-priori estimation.
Section IV shows the market risk premium in CAPM is decided by the expected excess rate of return on assets and the invertible covariance matrix
among the assets' rate of return.
T] is said to have the N-variate t distribution with degree of freedom [mu] with zero mean and R denoting covariance matrix
We examine this issue by comparing forecasts of the covariance matrix
obtained by means of a multivariate version of Corsi's Heterogeneous Auto-Regressive (HAR) model with the ones provided by traditional volatility models.
Given the above specification, the BEKK (p,q) model, with the conditional covariance matrix
t] is related to the conditional variance and covariance matrix
The covariance matrix
(14) is diagonal, thus it is assumed that the components of vector [X.