On the rate of convergence to a Poisson process

Let ξ = {ξ₁, ξ₂, ...} be a sequence of independent, spherically symmetric, identically distributed multivariate random vectors such that the condition

On the one-sided convergence of the Robbins-Monro process with small steps

In this paper, we consider the one-sided convergence of the Robbins-Monro process in the cases that have not been investigated earlier.     

On the concept of possibility-probability consistency

Both probability and possibility may be seen as information about an experiment. It is conceivable to have at some time these two forms of information about a same experiment and then the question of the relation between them arises at once. In this paper some aspects of the concept of possibility-probability consistency are studied. The consistency is considered as a fuzzy property relative to the coherence between possibilistic and probabilistic information. We analyse several measures of the degree of consistency and introduce an axiomatic to characterize them.     

On consistency of the likelihood moment estimators for a linear process with regularly varying innovations

In 1975 James Pickands III showed that the excesses over a high threshold are approximatly Generalized Pareto distributed. Since then, a variety of estimators for the parameters of this cdf have been studied, but always assuming the underlying data to be independent. In this paper we consider the special case where the underlying data arises from a linear process with regularly varying (i.e. heavy-tailed) innovations. Using this setup, we then show that the likelihood moment estimators introduced by Zhang Aust. N.Z. J. Stat. 49, 69–77 (2007) are consistent estimators for the parameters of the Generalized Pareto distribution.     

On the consistency of linear and quadratic systems

A system of linear inhomogeneous inequalities is examined. An algorithm is presented for isolating all the consistent subsystems in this system that are maximal with respect to inclusion, and justification of this algorithm is given. A criterion for the consistency of a system of quadratic inhomogeneous equations and inequalities is proposed.     

On the convergence of iterates

THIS PAPER points out that some of Thron's [5] results on the convergence of iterates of a real valued function of a real variable can be extended to general situations afforded, for instance, by metric and gauge spaces. A few examples are given at the end to illustrate the existence of the special type of operators dealt with in this paper.     

On the consistency of the Banzhaf semivalue

In this note we show that the Banzhaf semivalue is consistent with respect to a suitable reduced game which keeps a clear parallelism with that defined by Hart and Mas-Colell in (1989) to prove the consistency of the Shapley value. We also use this reduced game property to characterize the Banzhaf semivalue.     

On the convergence of SUMT

This paper investigates some convergence properties of Fiacco and McCormick's SUMT algorithm. A convex programming problem is given for which the SUMT algorithm generates a unique unconstrained minimizing trajectory having an infinite number of accumulation points, each a global minimizer to the original convex programming problem.     

On the convergence of the Bernstein — Grünwald averaging process for averaging interpolators

Acta Mathematica Hungarica -     

A Hidden-Markov estimation method for mean-shift detection of fraction defective in production process control

This paper considers a statistical method of estimating mean shift for a fraction defective of population. One traditional method for this estimation problem has been known as the CUSUM (cumulative sum) method, and it provides a method of estimating the occurrence of a shift in the mean from the observed data. We consider this estimation problem of shift occurrence in a production process. It is assumed that the process has two states, one is good (fraction defective low) and the other bad (fraction defective high), and starts in good state with probability one. We are interested in judging when the state has moved to the bad state by analyzing the observed data.In this paper, we model such a phenomenon as a hidden-Markov model. The states which are unobservable in a hidden-Markov model can be analyzed from the sequence of observed results. Hence, the advantage of this modeling technique is that the unknown parameters which are included in the hidden states can be estimated. We compare the performance of this hidden-Markov model with the CUSUM method based on several simulation data sets.     

A strong convergence to the Rosenblatt process

We give a strong approximation of Rosenblatt process via transport processes and we give the rate of convergence.