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This paper considers the properties of a minimum variance self-tuning tracker for MIMO systems described by ARMAX models. It is assumed that the stochastic noise has a non-Gaussian distribution. Such an assumption introduces into a recursive algorithm a nonlinear transformation of the prediction error. The system under consideration is minimum phase with different dimensions for input and output vectors. In the paper the concept of Kronecker's product is used, which allows us to represent unknown...
We discuss, partly on examples, several intuitively unexpected results in a standard linear regression model. We demonstrate that direct observations of the regression curve at a given point can not be substituted by observations at two very close neighboring points. On the opposite, we show that observations at two distant design points improve the variance of the estimator. In an experiment with correlated observations we show somewhat unexpected conditions under which a design point gives no...
The stress-strength model is proposed based on the -generalized order statistics and the corresponding concomitant. For the dependency between -generalized order statistics and its concomitant, a bivariate copula expansion is considered and the stress-strength model is obtained for two special cases of order statistics and upper record values. In the particular case of copula function, the generalized Farlie-Gumbel-Morgenstern bivariate distribution function is considered with proportional reversed...
Mixed models will be considered using the Commutative Jordan Algebra of Symmetric matrices approach. Prime basis factorial models will now be considered in the framework provided by Commutative Jordan Algebra of Symmetric matrices. This will enable to obtain fractional replicates when the number of levels is neither a prime or a power of a prime. We present an application to the effect of lidocaine, at an enzymatic level, on the heart muscle of beagle dogs
The strong convergence for weighted sums of widely orthant dependent (WOD) random variables is investigated. As an application, we further investigate the strong consistency of the least squares estimator in EV regression model for WOD random variables. A simulation study is carried out to confirm the theoretical results.
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