ﻻ يوجد ملخص باللغة العربية
We propose a new statistical test for the residual autocorrelation in ARX adaptive tracking. The introduction of a persistent excitation in the adaptive tracking control allows us to build a bilateral statistical test based on the well-known Durbin-Watson statistic. We establish the almost sure convergence and the asymptotic normality for the Durbin-Watson statistic leading to a powerful serial correlation test. Numerical experiments illustrate the good performances of our statistical test procedure.
The mixed fractional Vasicek model, which is an extended model of the traditional Vasicek model, has been widely used in modelling volatility, interest rate and exchange rate. Obviously, if some phenomenon are modeled by the mixed fractional Vasicek
The approximation of integral functionals with respect to a stationary Markov process by a Riemann-sum estimator is studied. Stationarity and the functional calculus of the infinitesimal generator of the process are used to get a better understanding
Consider a $p$-dimensional population ${mathbf x} inmathbb{R}^p$ with iid coordinates in the domain of attraction of a stable distribution with index $alphain (0,2)$. Since the variance of ${mathbf x}$ is infinite, the sample covariance matrix ${math
Marcinkiewicz strong law of large numbers, ${n^{-frac1p}}sum_{k=1}^{n} (d_{k}- d)rightarrow 0 $ almost surely with $pin(1,2)$, are developed for products $d_k=prod_{r=1}^s x_k^{(r)}$, where the $x_k^{(r)} = sum_{l=-infty}^{infty}c_{k-l}^{(r)}xi_l^{(r
An extension of the Gaussian correlation conjecture (GCC) is proved for multivariate gamma distributions (in the sense of Krishnamoorthy and Parthasarathy). The classical GCC for Gaussian probability measures is obtained by the special case with one degree of freedom.