A central limit theorem for linear

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

Central and Local Limit Theories in Markov Dependent Random Variables

Density Estimators for Truncated Dependent Data

In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for t...

Convergence of averages of scaled functions of I(1) linear processes

Econometricians typically make use of functional central limit theorems to prove results for I(1) processes. For example, to establish the limit distributions of unit root tests such as the Phillips–Perron and Dickey–Fuller tests, the functional central limit theorem plays a crucial role. In this paper, it is pointed out that for linear processes, minimal conditions that ensure that only a cent...

Central limit theorem for linear eigenvalue statistics of orthogonally invariant matrix models

We prove central limit theorem for linear eigenvalue statistics of orthogonally invariant ensembles of randommatrices with one interval limiting spectrum. We consider ensembles with real analytic potentials and test functions with two bounded derivatives.