between two coordinates of this random vector is also of interest: If it is bounded, then these two coordinates are asymptotically independent because of the joint normal distribution.
To calculate the probability of making a type I error in the LRT for the independence between two groups of variables, a computational simulation by the Monte Carlo method was performed, considering the following scenarios: 16 sample sizes--25, 30, 50, 100, 200, 300, 400, 500, 600, 750, 1,000, 1,500, 2,000, 3,000, 4,000 and 5,000; 40 combinations of the number of variables between the two groups--starting with 3+3, 3+4, 3+5, 3+6, 3+7, 3+8, 3+9, 3+10, 4+4, 4+5, 4+6, 4+7, 4+8, 4+9, 4+10, and 5+3 up to 14+10; and a degree of correlation between the variables of the covariance
To compare models with different nested covariance
structures, the Restricted Likelihood Ratio Test (RLRT) is used, as well as the BIC Criterion, since it penalizes models with a larger number of parameters.
Model 4 was the same as Model 3, but allowed for a direct maternal covariance
When the covariance
matrices are divided by selected suitable [[mu].
Given the expected excess rate of return vector R - r on n risky securities and the non-singular covariance
matrix [OMEGA] between n risky securities rate of returns, the portfolio [omega] in Equation (1) is the unique risky optimal mean-variance efficient within the mean-variance framework if and only if [omega] = [[OMEGA].
mul,1] during the derivation of the covariance
where i and j are the indices of the observed element in training and test covariance
matrices and N = 121 is the number of speakers in speech database.
T]) is the covariance
matrix of the collective premium vector
It is important to recall that these are not covariances
across levels of income sources, but rather the covariance
of income volatilities.
As mentioned in Section 1, the covariances
between growth-related parameters [alpha], [rho], and [delta] are directly influential upon the respective magnitudes of the ranges of variations of the functionally relevant parameters E, D, and K, according to the sign of the dependence of each parameter E, D, and K upon each parameter [alpha], [rho], and [delta] (signs of dependence provided at Table 1).
The authors test the model estimating the covariances
of returns of several portfolios with the market portfolio using the dynamic conditional correlation model (DCC) proposed by Engle (2002).