Related papers: Asymptotics for Markov chain mixture detection

We consider Markov chains on general state spaces in stationary random environment which are defined by a random mapping that is contractive up to a bounded perturbation. We prove their convergence to a limiting law, providing convergence…

Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…

In this paper, we consider the empirical spectral distribution of the sample correlation matrix and investigate its asymptotic behavior under mild assumptions on the data's distribution, when dimension and sample size increase at the same…

Estimating the mixing density of a latent mixture model is an important task in signal processing. Nonparametric maximum likelihood estimation is one popular approach to this problem. If the latent variable distribution is assumed to be…

Consider the likelihood ratio test (LRT) statistics for the independence of sub-vectors from a $p$-variate normal random vector. We are devoted to deriving the limiting distributions of the LRT statistics based on a random sample of size…

A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In our model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…

In this paper we investigate the asymptotic distribution of likelihood ratio tests in models with several groups, when the number of groups converges with the dimension and sample size to infinity. We derive central limit theorems for the…

We investigate a generalized empirical likelihood approach in a two-group setting where the constraints on parameters have a form of U-statistics. In this situation, the summands that consist of the constraints for the empirical likelihood…

It is common practice in Markov chain Monte Carlo to update the simulation one variable (or sub-block of variables) at a time, rather than conduct a single full-dimensional update. When it is possible to draw from each full-conditional…

A family $\{Q_{\beta}\}_{\beta \geq 0}$ of Markov chains is said to exhibit $\textit{metastable mixing}$ with $\textit{modes}$ $S_{\beta}^{(1)},\ldots,S_{\beta}^{(k)}$ if its spectral gap (or some other mixing property) is very close to the…

We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g. exchangeable observational units or features) and contiguous groups, or…

Assume that one observes the $k$th, $2k$th$,\ldots,nk$th value of a Markov chain $X_{1,h},\ldots,X_{nk,h}$. That means we assume that a high frequency Markov chain runs in the background on a very fine time grid but that it is only observed…

For near-critical, transient Markov chains on the non-negative integers in the Lamperti regime, where the mean drift at $x$ decays as $1/x$ as $x \to \infty$, we quantify degree of transience via existence of moments for conditional return…

To understand how hidden information can be extracted from statistical networks, planted models in random graphs have been the focus of intensive study in recent years. In this work, we consider the detection of a planted matching, i.e., an…

This article proposes a method to quantify the structure of a bipartite graph using a network entropy per link. The network entropy of a bipartite graph with random links is calculated both numerically and theoretically. As an application…

For downward skip-free continuous-time Markov chains on non-negative integers stopped at zero, existence of a quasi-stationary distribution is studied. The scale function for these processes is introduced and the boundary is classified by a…

We consider a strictly substochastic matrix or an stochastic matrix with absorbing states. By using quasi-stationary distributions one shows there is a canonical associated stationary Markov chain. Based upon $2-$stringing representation of…

We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…

We consider the problem of detecting a general sparse mixture and obtain an explicit characterization of the phase transition under some conditions, generalizing the univariate results of Cai and Wu. Additionally, we provide a sufficient…

We consider tilings of $\mathbb{Z}^2$ by two types of squares. We are interested in the rate of convergence to the stationarity of a natural Markov chain defined for square tilings. The rate of convergence can be represented by the mixing…