Related papers: Testing the mixture model hypothesis via spectral …

We study the problem of mapping an unknown mixed quantum state onto a known pure state without the use of unitary transformations. This is achieved with the help of sequential measurements of two non-commuting observables only. We show that…

The ability to quantify distinctness of a cluster structure is fundamental for certain simulation studies, in particular for those comparing performance of different classification algorithms. The intrinsic integral measure based on the…

We consider the gauging of $L_\mu - L_\tau$ as an explanation of a possibly large muon anomalous magnetic moment. We then show how neutrino masses with bimaximal mixing may be obtained in this framework. We study the novel phenomenology of…

In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…

We are concerned with an harmonic analysis in Hilbert spaces $L^2(\mu)$, where $\mu$ is a probability measure on $\br^n$. The unifying question is the presence of families of orthogonal (complex) exponentials $e_\lambda(x) = \exp(2\pi i…

We analyse the largest eigenvalue of the adjacency matrix of the configuration model with large degrees, where the latter are treated as hard constraints. In particular, we compute the expectation of the largest eigenvalue for degrees that…

We study the problem of mismatched likelihood ratio test. We analyze the type-\RNum{1} and \RNum{2} error exponents when the actual distributions generating the observation are different from the distributions used in the test. We derive…

The conditional independence assumption has recently appeared in a growing body of literature on the estimation of multivariate mixtures. We consider here conditionally independent multivariate mixtures of power series distributions with…

The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function…

Let $\mu$ be a log-concave probability measure on ${\mathbb R}^n$ and for any $N>n$ consider the random polytope $K_N={\rm conv}\{X_1,\ldots ,X_N\}$, where $X_1,X_2,\ldots $ are independent random points in ${\mathbb R}^n$ distributed…

A Gaussian measurement error assumption, i.e., an assumption that the data are observed up to Gaussian noise, can bias any parameter estimation in the presence of outliers. A heavy tailed error assumption based on Student's t distribution…

In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…

Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is…

We study the stationary measures for variants of the Porous Medium Model in dimension 1. These are exclusion processes that belong to the class of kinetically constrained models, in which an exchange can occur between $x$ and $x+1$ only if…

We consider the following convolution equation or equivalently stochastic difference equation $$\lam _k = \mu _k*\phi (\lam _{k-1}), k \in \Z \eqno (1) $$ for a given bi-sequence $(\mu _k)$ of probability measures on $\R ^d$ and a linear…

This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g. all pairwise Kendall's $\tau$) between the components…

Let $(E,\mathcal F,\mu)$ be a probability space, and let $P$ be a Markov operator on $L^2(\mu)$ with $1$ a simple eigenvalue such that $\mu P=\mu$ (i.e. $\mu$ is an invariant probability measure of $P$). Then $\hat P:=\ff 1 2 (P+P^*)$ has a…

We consider the apparatus in a quantum measurement process to be in a mixed state. We propose a simple upper bound on the probability of correctly distinguishing any number of mixed states. We use this to derive fundamental bounds on the…

We study self-similar measures in $\mathbb{R}$ satisfying the weak separation condition along with weak technical assumptions which are satisfied in all known examples. For such a measure $\mu$, we show that there is a finite set of concave…

A mixture with varying concentrations is a modification of a finite mixture model in which the mixing probabilities (concentrations of mixture components) may be different for different observations. In the paper, we assume that the…