cerebellar model articulation controller neural network is a computational model of cerebellum which acts as a lookup table. the advantages of cmac are fast learning convergence, and capability of mapping nonlinear functions due to its local generalization of weight updating, single structure and easy processing. in the training phase, the disadvantage of some cmac models is unstable phenomenon...

We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of any even order converge in the almost sure central limit theorem for martingales. A conjecture about almost sure upper bounds under wider hypotheses is formul...

We obtain rates of convergence and asymptotic expansions in limit theorems for powers of reciprocals of random variables. Our results improve on recent work of Shapiro [18], who obtained Berry-Esseen bounds of order n~ l/9+c (e > 0). Under weaker conditions than Shapiro imposed we obtain asymptotic expansions whose first term is of order n~ i (logn) 2 .

One of the generalizations of statistical convergence is I-convergence which was introduced by Kostyrko et al. [12]. In this paper, we define and study the concept of I-convergence, I∗-convergence, I-limit points and I-cluster points of double sequences in probabilistic normed space. We discuss the relationship between I2-convergence and I ∗ 2 -convergence, i.e., we show that I ∗ 2 -convergence...

we have by construction μ(En) = an. An important observation is that a subset of consecutive intervals En, En+1, . . . , En+k are either pairwise disjoint, or they cover the whole interval [0, 1]. Now for all n, let fn = 1En . Then we have • ‖fn‖1 = ∫ X |1En |dμ = μ(En) = an. • for all x ∈ [0, 1], (fn(x))n does not converge. Indeed, if we suppose by contradiction that (fn(x))n converges for som...

The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical density. We will also obtain a sharp rate of convergence to the normal distribution for the central limit theorem. Some generalizations are provided.

In investigations on the behaviour of robust estimators, typically their consistency and their asymptotic normality are studied as a necessity. Their rates of convergence, however, are often given less weight. We show here that the rate of convergence of a multivariate robust estimator to its true value plays an important role when using the estimator in procedures for identifying outliers in m...

In the present paper we give the rate of convergence for the linear combinations of the generalized Durrmeyer type operators which includes the well known Szasz-Durrmeyer operators and Baskakov-Durrmeyer operators as special cases.

We study the convergence of mating operators on {0, 1}n. In particular, we answer questions of Rabani, Rabinovich and Sinclair (cf. [5]) by giving tight estimates on the divergence between the finiteand infinite-population processes, thus solving positively the problem of the simulability of such quadratic dynamical systems. c © (Year) John Wiley & Sons, Inc.