We implement the recently introduced Poisson approximation on a density dependent jump process corresponding to a simple, but not exactly solvable, epidemiological model. Statistics produced with 10 independent realizations of the Feller process are compared with equivalent statistics produced with Poisson, proper Gaussian and diffusion realizations. While in the Poisson approximation the stati...

We introduce a new form of nonlinear approximation called restricted approximation. It is a generalization of n-term wavelet approximation in which a weight function is used to control the terms in the wavelet expansion of the approximant. This form of approximation occurs in statistical estimation and in the characterization of interpolation spaces for certain pairs of L p and Besov spaces. We...

In this paper we consider the notion of A2 -statistical convergence for real double sequences which is an extension of the notion of AI -statistical convergence for real single sequences introduced by Savas, Das and Dutta. We primarily apply this new notion to prove a Korovkin type approximation theorem. In the last section, we study the rate of A2 -statistical convergence.

We first construct a sequence of double smooth Picard singular integral operators which do not have to be positive in general. After giving some useful estimates, we mainly show that it is possible to approximate a function by these operators in statistical sense even though they do not obey the positivity condition of the statistical Korovkin theory.

Given a set P of n points in Rd, a fundamental problem in computational geometry is concerned with finding the smallest shape of some type that encloses all the points of P . Well-known instances of this problem include finding the smallest enclosing box, minimum volume ball, and minimum volume annulus. In this paper we consider the following variant: Given a set of n points in Rd, find the sma...

In this paper, we prove some approximation results in statistical sense and establish some direct theorems for the positive linear operators constructed by the means Lagrange type polynomials. We compute error estimation by using modulus of continuity with the help of Matlab and give its algorithm. Furthermore, we show graphically the convergence of our operators to various functions. AMS Subje...

Decomposition in a basis: (b j) j∈J basis of L 2 ([0, 1]). ∀f ∈ L 2 ([0, 1], f = j∈J f, b j b j with f, b j = 1 0 f (t)b j (t)dt. The Parseval-Bessel norm energy conservation equality yields f 2 = j∈J |f, b j | 2 1.2 Linear and non linear approximation For any I ∈ P(J), one defines f |I by f |I = j∈I f, b j b j. The question is now how to select " a good subset " of a given size M. A first poss...

Let A = (a jn) be an infinite summability matrix. For a given sequence x := (xn), the A-transform of x, denoted by Ax := ((Ax) j), is given by (Ax) j = ∑n=1 a jnxn provided the series converges for each j ∈ N, the set of all natural numbers. We say that A is regular if limAx = L whenever limx = L [4]. Assume that A is a non-negative regular summability matrix. Then x = (xn) is said to be A-stat...

Statistical and probabilistic characteristics of locally free group with growing number of generators are defined and their application to statistics of braid groups is given.

In this paper, a statistical approximation learning (SAL) method is proposed for a new type of neural networks, simultaneous recurrent networks (SRNs). The SRNs have the capability to approximate non-smooth functions which cannot be approximated by using conventional multi-layer perceptrons (MLPs). However, the most of the learning methods for the SRNs are computationally expensive due to their...