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Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting, suppose we wish to solve the following…
We investigate the spectral distribution of large sample covariance matrices with independent columns and entries in the columns that stem from Markov chains. We characterize the limiting spectral densities by their moments.…
Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we consider the…
Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random…
In this paper we develop a statistical estimation technique to recover the transition kernel $P$ of a Markov chain $X=(X_m)_{m \in \mathbb N}$ in presence of censored data. We consider the situation where only a sub-sequence of $X$ is…
Distribution estimation under error-prone or non-ideal sampling modelled as "sticky" channels have been studied recently motivated by applications such as DNA computing. Missing mass, the sum of probabilities of missing letters, is an…
We consider a class of small-sample distribution estimators over noisy channels. Our estimators are designed for repetition channels, and rely on properties of the runs of the observed sequences. These runs are modeled via a special type of…
In this paper, we study the hypothesis testing problem of, among $n$ random variables, determining $k$ random variables which have different probability distributions from the rest $(n-k)$ random variables. Instead of using separate…
The analysis of high-dimensional time series data has become increasingly important across a wide range of fields. Recently, a method for constructing the minimum information Markov kernel on finite state spaces was established. In this…
In this work, we study non-parametric hypothesis testing problem with distribution function constraints. The empirical likelihood ratio test has been widely used in testing problems with moment (in)equality constraints. However, some…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
Multivariate data sources with components of different information value seem to appear frequently in practice. Models in which the components change their homogeneity at different times are of significant importance. The fact whether any…
A statistical test is presented to decide whether data are adequately described by probabilistic functions of finite state Markov chains (''hidden Markov models'') as applied in the analysis of ion channel data. Particularly, the test can…
We develop a testing procedure for distinguishing between a long-range dependent time series and a weakly dependent time series with change-points in the mean. In the simplest case, under the null hypothesis the time series is weakly…
Score-based diffusion models, while achieving minimax optimality for sampling, are often hampered by slow sampling speeds due to the high computational burden of score function evaluations. Despite the recent remarkable empirical advances…
The problem of the estimation of relevance to a set of histograms generated by samples of a discrete time process is discussed on the base of the variational principles proposed in the previous paper [1]. Some conditions for dimension…
One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady state when the two velocities and/or the two switching rates are space-dependent. A long dynamical trajectory can be then analyzed via the…
A collaborative distributed binary decision problem is considered. Two statisticians are required to declare the correct probability measure of two jointly distributed memoryless process, denoted by $X^n=(X_1,\dots,X_n)$ and…
Consider the problem of binary hypothesis testing. Given $Z$ coming from either $\mathbb P^{\otimes m}$ or $\mathbb Q^{\otimes m}$, to decide between the two with small probability of error it is sufficient, and in many cases necessary, to…
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…