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We develop a clustering framework for observations from a population with a smooth probability distribution function and derive its asymptotic properties. A clustering criterion based on a linear combination of order statistics is proposed.…
We compute the expected number of commutations appearing in a reduced word for the longest element in the symmetric group. The asymptotic behavior of this value is analyzed and shown to approach the length of the permutation, meaning that…
Asymptotic properties of a vector of length power functionals of random geometric graphs are investigated. More precisely, its asymptotic covariance matrix is studied as the intensity of the underlying homogeneous Poisson point process…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight…
We consider linear codes over a finite field of odd characteristic, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a code word is derived. Using this formula, we have…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
This paper is the second part of the study. In Part~I, self-similar solutions of a weighted fast diffusion equation (WFD) were related to optimal functions in a family of subcritical Caffarelli-Kohn-Nirenberg inequalities (CKN) applied to…
In this paper, we derive variational formulas for the asymptotic exponents (i.e., convergence rates) of the concentration and isoperimetric functions in the product Polish probability space under certain mild assumptions. These formulas are…
The article studies the almost surely asymptotics of extreme values $\bar{\xi}_n = \max_{1\leq i \leq n} \xi_i$, where $ \xi , \xi_1 , \xi_2 , \ldots$ are discrete identically distributed random variables. One of the main results on this…
In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower (existence) bound for stabilizer codes is proved by a…
A new lower bound on the error probability of maximum likelihood decoding of a binary code on a binary symmetric channel was proved in Barg and McGregor (2004, cs.IT/0407011). It was observed in that paper that this bound leads to a new…
Recent works have shown an interest in investigating the frequentist asymptotic properties of Bayesian procedures for high-dimensional linear models under sparsity constraints. However, there exists a gap in the literature regarding…
We consider (symmetric, non-degenerate) bilinear spaces over a finite field and investigate the properties of their $\ell$-complementary subspaces, i.e., the subspaces that intersect their dual in dimension $\ell$. This concept generalizes…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
Using operator methods, we generally present the level densities for kinds of random matrix unitary ensembles in weak sense. As a corollary, the limit spectral distributions of random matrices from Gaussian, Laguerre and Jacobi unitary…
We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…
The goal of the paper is to study asymptotic behavior of the number of lost messages. Long messages are assumed to be divided into a random number of packets which are transmitted independently of one another. An error in transmission of a…
Weighted empirical risk minimization is a common approach to prediction under distribution drift. This article studies its out-of-sample prediction error under nonstationarity. We provide a general decomposition of the excess risk into a…
Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…