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Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
A new probability distribution to study lifetime data in reliability is introduced in this paper. This one is a first approach to a non-homogeneous phase-type distribution. It is built by considering one cut-point in the non-negative…
In recent years, there has been an increasing demand on efficient algorithms for large scale change point detection problems. To this end, we propose seeded binary segmentation, an approach relying on a deterministic construction of…
We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.
In this paper, we study the offline change point localization problem in a sequence of dependent nonparametric random dot product graphs. To be specific, assume that at every time point, a network is generated from a nonparametric random…
Spatio-temporal point process (STPP) is a stochastic collection of events accompanied with time and space. Due to computational complexities, existing solutions for STPPs compromise with conditional independence between time and space,…
Chatteerjee and Diaconis have recently shown the asymptotic normality for the joint distribution of the number of descents and inverse descents in a random permutation. A noteworthy point of their results is that the asymptotic variance of…
This paper studies distributed adaptive estimation over sensor networks with partially unknown source dynamics. We present parallel continuous-time and discrete-time designs in which each node runs a local adaptive observer and exchanges…
We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
This paper examines the joint problem of detection and identification of a sudden and unobservable change in the probability distribution function (pdf) of a sequence of independent and identically distributed (i.i.d.) random variables to…
We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…
For a variety of pattern-avoiding classes, we describe the limiting distribution for the number of fixed points for involutions chosen uniformly at random from that class. In particular we consider monotone patterns of arbitrary length as…
In this paper, we consider semi-Markov processes whose transition times and transition probabilities depend on a small parameter $\varepsilon$. Understanding the asymptotic behavior of such processes is needed in order to study the…
In this article, a new mathematical model of human population growth as an autonomous non-Markov queuing system with an unlimited number of servers and two types of applications is proposed. The research of this system was carried out a…
Change point analysis has become an important research topic in many fields of applications. Several research work has been carried out to detect changes and its locations in time series data. In this paper, a nonparametric method based on…
We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…
Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…
Changepoints are abrupt variations in the generative parameters of a data sequence. Online detection of changepoints is useful in modelling and prediction of time series in application areas such as finance, biometrics, and robotics. While…