The present paper deals with least weighted squares estimator which is a robust estimator and it generalizes classical least trimmed squares. We will prove -consistency and asymptotic normality for any sequence of roots of normal equation for location model. The influence function for general case is calculated. Finally optimality of this estimator is discussed and formula for most B-robust and most V-robust weights is derived.
The paper continues our studies released under the same title [Andres, J., Kubáček, L., Machalová, J., Tučková, M.: Optimization of parameters in the Menzerath–Altmann law Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 51, 1 (2012), 5–27.]. As the main result justifying the conclusions in [Andres, J., Kubáček, L., Machalová, J., Tučková, M.: Optimization of parameters in the Menzerath–Altmann law Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 51, 1 (2012), 5–27.], the theorem is presented...
Outliers in univariate and multivariate regression models with constraints are under consideration. The covariance matrix is assumed either to be known or to be known only partially.
This paper is concerned with the problem of global state regulation by output feedback for large-scale uncertain nonlinear systems with time delays in the states and inputs. The systems are assumed to be bounded by a more general form than a class of feedforward systems satisfying a linear growth condition in the unmeasurable states multiplying by unknown growth rates and continuous functions of the inputs or delayed inputs. Using the dynamic gain scaling technique and choosing the appropriate Lyapunov-Krasovskii...
The problem of estimating the number, n, of trials, given a sequence of k independent success counts obtained by replicating the n-trial experiment is reconsidered in this paper. In contrast to existing methods it is assumed here that more information than usual is available: not only the numbers of successes are given but also the number of pairs of consecutive successes. This assumption is realistic in a class of problems of spatial statistics. There typically k = 1, in which case the classical...
In this paper, we present a parameter estimation method for sub-Gaussian stable distributions. Our algorithm has two phases: in the first phase, we calculate the average values of harmonic functions of observations and in the second phase, we conduct the main procedure of asymptotic maximum likelihood where those average values are used as inputs. This implies that the main procedure of our method does not depend on the sample size of observations. The main idea of our method lies in representing...
Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed. This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measurement instants. A tuned...
The problem of testing hypothesis under which the observations are independent, identically distributed against a class of alternatives of regression in a parameter of the one-parameter exponential family is studied. A parametric test for this problem is suggested. The relative efficiency of the parametric test compared to the rank test proposed in the author's preceding paper is also derived.