Related papers: Le Cam spacings theorem in dimension two
This paper provides two characterizations of regularity for near-vector spaces: first, by expressing them as a direct sum of vector spaces over division rings formed by distributive elements; second, by expressing their dimension in term of…
We consider the invariance principle without the classical condition of asymptotic negligibility of individual terms. More precisely, we explore the difference of the following two distributions in the space C (of continuous functions on…
We consider the continued fraction expansion of real numbers under the action of a non-uniform lattice in PSL(2,R) and prove metric relations between the convergents and a natural geometric notion of good approximations.
In this research article, we have primarily focused on the circumstantial investigation of deferred statistical convergence of sequences and investigated some fundamental results compatible with the structure of a probabilistic normed…
This paper concerns a long-standing problem raised by Beurling and Wintner on completeness of the dilation system $\{\varphi(kx):k=1,2,\cdots\}$ generated by the odd periodic extension on $\mathbb{R}$ of any $\varphi\in L^2[0,1]$. Up to now…
The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song \emph{et al.}, Nature (London) {\bf 453}, 629 (2008)] is generalized to arbitrary dimension $d$ using a liquid-state description. The…
We say that a random vector $X=(X_1,...,X_n)$ in $R^n$ is an $n$-dimensional version of a random variable $Y$ if for any $a\in R^n$ the random variables $\sum a_iX_i$ and $\gamma(a) Y$ are identically distributed, where $\gamma:R^n\to…
Tests based on sample mean vectors and sample spatial signs have been studied in the recent literature for high dimensional data with the dimension larger than the sample size. For suitable sequences of alternatives, we show that the powers…
Stein's method is used to obtain two theorems on multivariate normal approximation. Our main theorem, Theorem 1.2, provides a bound on the distance to normality for any nonnegative random vector. Theorem 1.2 requires multivariate size bias…
In (hyper)coherence semantics, proofs/terms are cliques in (hyper)graphs. Intuitively, vertices represent results of computations and the edge relation witnesses the ability of being assembled into a same piece of data or a same (strongly)…
Let $(X,d)$ be a proper ultrametric space. Given a measure $m$ on $X$ and a function $C(B)$ defined on the set of all non-singleton balls $B$ we consider the hierarchical Laplacian $L=L_{C}$. Choosing a sequence $\{\varepsilon (B)\}$ of…
Self-similarity of systems is very popular and intensively developing field during last decades. To this field belong so-called stable distributions and their generalization. In Klebanov and Sl\'amov\'a (2014) there was given an approach to…
Consider a random sample of $n$ independently and identically distributed $p$-dimensional normal random vectors. A test statistic for complete independence of high-dimensional normal distributions, proposed by Schott (2005), is defined as…
Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses M\"obius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory.…
We discuss various forms of the Luxemburg norm in spaces of random vectors with coordinates belonging to the classical Orlicz spaces of exponential type. We prove equivalent relations between some kinds of these forms. We also show when the…
A tantalizing conjecture in discrete mathematics is the one of Koml\'os, suggesting that for any vectors $\mathbf{a}_1,\ldots,\mathbf{a}_n \in B_2^m$ there exist signs $x_1, \dots, x_n \in \{ -1,1\}$ so that $\|\sum_{i=1}^n…
In this appendix to our paper with the same title posted on arxiv we give a quick proof of an inequality that can be substituted to Hastings's result, quoted as Lemma 1.9 in our previous paper. Our inequality is less sharp but also appears…
We consider a general class of statistical experiments, in which an $n$-dimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be…
Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables…
The distribution function of a random distance in three dimensions is given and some new three-dimensional d2-tests of randomness are suggested. We show that our test statistics are not correlated with the usual test statistics and are…