A flexible class of anisotropic stationary lattice processes with long memory can be defined in terms of a two-way fractional ARIMA (FARIMA) representation. We consider parameter estimation based on minimizing an approximate residual sum of squares. The method can be applied to sampling areas...

A new approach to tail index estimation based on huberization of the Pareto MLE is considered. The proposed estimator is robust in a nonstandard way in that it protects against deviations from the central model at low quantiles. Asymptotic normality with the parametric n-rate of convergence is...

The aim of this paper is to give exact LR testing procedures of the homogeneity and scale hypotheses for the widely used loss distributions Gamma and Weibull. We derive the exact distributions of such tests and also provide some their properties.

In the present paper we provide a thorough study of small sample and asymptotical comparisons of the efficiencies of equidistant designs taking into account both the parameters of trend [theta], as well as the parameters of covariance function r of the Ornstein-Uhlenbeck process. If only trend...

Computer simulations are often used to replace physical experiments for exploring the complex relationships between input and output variables. We study the optimal design problem for the prediction of a stationary Ornstein–Uhlenbeck sheet on a monotonic set with respect to the integrated mean...

The problem that assets of a fund are not suffi cient to cover its liabilities is of extreme importance both for its members as well as for fund managers. We show that this problem can be solved via total claims distributions and give answers to the following questions: How much money will be...