Mindaugas Bloznelis

A Berry-Esséen bound for student's statistic in the non-I.I.D. case

We establish a Berry-Esséen bound for Students statistic for independent (nonidentically) distributed random variables. In particular, the bound implies a sharp estimate similar to the classical Berry-Esséen bound. In the i.i.d. case it yields sufficient conditions for the Central Limit Theorem for studentized sums. For non-i.i.d. random variables the bound shows that the Lindeberg condition is sufficient for the Central Limit Theorem for studentized sums.

An Edgeworth expansion for finite-population U-statistics

Suppose that U is a U-statistic of degree 2 based on N random observations drawn without replacement from a finite population. For the distribution of a standardized version of U we construct an Edgeworth expansion with remainder O(N-1) provided that the linear part of the statistic satisfies a Cramer type condition.

Recent Progress in Complex Network Analysis: Properties of Random Intersection Graphs

Experimental results show that in large complex networks (such as internet, social or biological networks) there exists a tendency to connect elements which have a common neighbor. In theoretical random graph models, this tendency is described by the clustering coefficient being bounded away from zero. Complex networks also have power-law degree distributions and short average distances (small world phenomena). These are desirable features of random graphs used for modeling real life networks. We survey recent results concerning various random intersection graph models showing that they have tunable clustering coefficient, a rich class of degree distributions including power-laws, and short average distances.

On the central limit theorem in D[0, 1]

Let X be a stochastically continuous random process with sample paths in D[0, 1]. We improve Billingsleys theorem and this improvement yields new sufficient conditions for X to satisfy the CLT. An example shows that our sufficient conditions are close to the optimal conditions of the form provided.

Component Evolution in General Random Intersection Graphs

Given integers

A random intersection digraph: Indegree and outdegree distributions

n

Orthogonal Decomposition of Symmetric Functions Defined on Random Permutations

,

Empirical Edgeworth Expansion for Finite Population Statistics. II

m

One-Term Edgeworth Expansion for Finite Population U-Statistics of Degree Two

and a probability distribution

SECOND-ORDER AND BOOTSTRAP APPROXIMATION TO STUDENT'S t-STATISTIC ∗

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