Related papers: Statistical Inference in Parametric Preferential A…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible…
This paper is concerned with statistical estimation of two preferential attachment models: the Buckley-Osthus model and the hierarchical preferential attachment model. We prove that the maximum likelihood estimates for both models are…
Eliciting preferences from human judgements is inherently imprecise, yet most decision analysis methods force a single priority vector from pairwise comparisons, discarding the information embedded in inconsistencies. We instead leverage…
Preferential attachment is commonly invoked to explain the emergence of those heavy-tailed degree distributions characteristic of growing network representations of diverse real-world phenomena. Experimentally confirming this hypothesis in…
We study the asymptotic diameter of the preferential attachment model $\operatorname{PA}\!_n^{(m,\delta)}$ with parameters $m \ge 2$ and $\delta > 0$. Building on the recent work \cite{VZ25}, we prove that the diameter of $G_n \sim…
Extreme value theory has constructed asymptotic properties of the sample maximum. This study concerns probability distribution estimation of the sample maximum. The traditional approach is parametric fitting to the limiting distribution --…
The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…
The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…
We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a…
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…
A large number of explicit estimators are proposed in this paper for loss rate estimation in a network of the tree topology. All of the estimators are proved to be unbiased and consistent instead of asymptotic unbiased as that obtained in…
We show that to explain the growth of the citation network by preferential attachment (PA), one has to accept that individual nodes exhibit heterogeneous fitness values that decay with time. While previous PA-based models assumed either…
The paper studies the problem of distributed parameter estimation in multi-agent networks with exponential family observation statistics. A certainty-equivalence type distributed estimator of the consensus + innovations form is proposed in…
Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. Practical analyses on the tail exponent of the power-law degree distribution use the Hill estimator as one…
Under preferential attachment (PA) network growth models late arrivals are at a disadvantage with regard to their final degrees. Previous extensions of PA have addressed this deficiency by either adding the notion of node fitness to PA,…
Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we…
Inference on the parametric part of a semiparametric model is no trivial task. If one approximates the infinite dimensional part of the semiparametric model by a parametric function, one obtains a parametric model that is in some sense…
In this paper, we propose a growing random complex network model, which we call context dependent preferential attachment model (CDPAM), when the preference of a new node to get attached to old nodes is determined by the local and global…