Related papers: Large deviations and exact asymptotics for constra…
The unconstrained exponential family of random graphs assumes no prior knowledge of the graph before sampling, but it is natural to consider situations where partial information about the graph is known, for example the total number of…
We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations,…
We propose a perturbative method to estimate the normalization constant in exponential random graph models as the weighting parameters approach infinity. As an application, we give evidence of discontinuity in natural parametrization along…
We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the limiting probability distribution and the…
We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…
We derive asymptotic formulas for central extended binomial coefficients, which are generalizations of binomial coefficients. To do so, we relate the exact distribution of the sum of independent discrete uniform random variables to the…
In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that there exists non-trivial regions in the phase plane where the…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
The question of whether the central limit theorem (CLT) holds for the total number of edges in exponential random graph models (ERGMs) in the subcritical region of parameters has remained an open problem. In this paper, we establish the…
In this paper non-asymptotic exact exponential estimates are derived (under minimal conditions) for the tail of deviation of the MLE distribution in the so-called natural terms: natural function, natural distance, metric entropy, Banach…
The purpose of this article is to present a general method to find limiting laws for some renormalized statistics on random permutations. The model considered here is Ewens sampling model, which generalizes uniform random permutations. We…
In this paper non-asymptotic exact exponential estimates are derived for the tail of maximum distribution of random field in the terms of majoring measures or, equally, generic chaining.
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
We characterize some asymptotic properties of edge exchangeable random graphs in terms of the measure used to generate them. In particular, we give a necessary and sufficient condition for eventual forever connectedness, a sufficient…
We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…
We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint…
In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties…
We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained…