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An orientable sequence of order $n$ is a cyclic binary sequence such that each length-$n$ substring appears at most once \emph{in either direction}. Maximal length orientable sequences are known only for $n\leq 7$, and a trivial upper bound…
Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…
The problem of joint detection and lossless source coding is considered. We derive asymptotically optimal decision rules for deciding whether or not a sequence of observations has emerged from a desired information source, and to compress…
We consider the Random Euclidean Assignment Problem in dimension $d=1$, with linear cost function. In this version of the problem, in general, there is a large degeneracy of the ground state, i.e. there are many different optimal matchings…
Discrete random probability measures are a key ingredient of Bayesian nonparametric inferential procedures. A sample generates ties with positive probability and a fundamental object of both theoretical and applied interest is the…
For a skew normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an…
We study two types of probability measures on the set of integer partitions of $n$ with at most $m$ parts. The first one chooses the random partition with a chance related to its largest part only. We then obtain the limiting distributions…
In this paper, we consider approximating expansions for the distribution of integer valued random variables, in circumstances in which convergence in law cannot be expected. The setting is one in which the simplest approximation to the…
A sequential design problem for rank aggregation is commonly encountered in psychology, politics, marketing, sports, etc. In this problem, a decision maker is responsible for ranking $K$ items by sequentially collecting pairwise noisy…
This paper is interested in independent sets (or equivalently, cliques) in uniform random cographs. We also study their permutation analogs, namely, increasing subsequences in uniform random separable permutations. First, we prove that,…
Sequential likelihood ratio testing is found to be most powerful in sequential studies with early stopping rules when grouped data come from the one-parameter exponential family. First, to obtain this elusive result, the probability measure…
A determinantal approximation is obtained for the permanent of a doubly stochastic matrix. For moderate-deviation matrix sequences, the asymptotic relative error is of order $O(n^{-1})$.
Random permutations with distribution conditionally uniform given the set of record values can be generated in a unified way, coherently for all values of $n$. Our central example is a two-parameter family of random permutations that are…
We investigate the approximation for computing the sum $a_1+...+a_n$ with an input of a list of nonnegative elements $a_1,..., a_n$. If all elements are in the range $[0,1]$, there is a randomized algorithm that can compute an…
We study higher order convexity properties of random point sets in the unit square. Given $n$ uniform i.i.d random points, we derive asymptotic estimates for the maximal number of them which are in $k$-monotone position, subject to mild…
A sequence of reversals that takes a signed permutation to the identity is perfect if at no step a common interval is broken. Determining a parsimonious perfect sequence of reversals that sorts a signed permutation is NP-hard. Here we show…
Probability estimation is essential for every statistical data compression algorithm. In practice probability estimation should be adaptive, recent observations should receive a higher weight than older observations. We present a…
We characterize the minimum-length sequences of independent lazy simple transpositions whose composition is a uniformly random permutation. For every reduced word of the reverse permutation there is exactly one valid way to assign…
Let M=M(n,q) be the average of the orders of the elements in the finite unitary group U(n,q). The asymptotic estimate log(M)=nlog(q)-log(n) +o(log n) is proved.
We study sequential multiple testing with independent data streams, where the goal is to identify an unknown subset of signals while controlling commonly used error metrics, including generalized familywise rates and false discovery and…