Related papers: Sequences of expected record values
A new class of integer-valued autoregressive models with dynamic survival probability is proposed. The peculiarity of this class of models lies on the specification of the survival probability through a stochastic recurrence equation. The…
We define a moment-based estimator that maximizes the empirical saddlepoint (ESP) approximation of the distribution of solutions to empirical moment conditions. We call it the ESP estimator. We prove its existence, consistency and…
There is a growing need for the ability to analyse interval-valued data. However, existing descriptive frameworks to achieve this ignore the process by which interval-valued data are typically constructed; namely by the aggregation of…
As artificial intelligence and machine learning tools become more accessible, and scientists face new obstacles to data collection (e.g. rising costs, declining survey response rates), researchers increasingly use predictions from…
We consider a Sturm-Liouville operator on a finite interval as well as a scattering problem on the real line both with transfer conditions at the origin. On a finite interval we show that the the Titchmarsh-Weyl $m$-function can be uniquely…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
The problem of demand inversion - a crucial step in the estimation of random utility discrete-choice models - is equivalent to the determination of stable outcomes in two-sided matching models. This equivalence applies to random utility…
The absolute moments of probability distributions are much more complicated than conventional ones. By using a direct and simpler approach, we retreat P. L. Hsu's (1951, J. Chinese Math. Soc., Vol. 1, pp. 257-280) formulas in terms of the…
Inversion sequences are integer sequences $(\sigma_1, \dots, \sigma_n)$ such that $0 \leqslant \sigma_i < i$ for all $1 \leqslant i \leqslant n$. The study of pattern-avoiding inversion sequences began in two independent articles by…
Let $(X_t)_{t \geq 0}$ be a continuous time Markov process on some metric space $M,$ leaving invariant a closed subset $M_0 \subset M,$ called the {\em extinction set}. We give general conditions ensuring either "Stochastic persistence"…
The analysis of dynamical systems is a fundamental tool in the natural sciences and engineering. It is used to understand the evolution of systems as large as entire galaxies and as small as individual molecules. With predefined conditions…
For any integer $k\geq 1,$ define $L_k: \mathbb{R}^\mathbb{N}\to \mathbb{R}^\mathbb{N}$ by $(a_n)_{n\in\mathbb{N}}\mapsto (a'_n)_{n\in\mathbb{N}}$ where $a'_n=\det(a_{n+i+j})_{i,j=0}^{k-1}$. Previously, Zhu showed that $L_k$ preserves the…
The problem of sequential anomaly detection is considered, where multiple data sources are monitored in real time and the goal is to identify the "anomalous" ones among them, when it is not possible to sample all sources at all times. A…
Given a set of aligned sequences of independent noisy observations, we are concerned with detecting intervals where the mean values of the observations change simultaneously in a subset of the sequences. The intervals of changed means are…
We study the exact constants in the moment inequalities for sums of centered independent random variables: improve their asymptotics, low and upper bounds, calculate more exact asymptotics, elaborate the numerical algorithm for their…
We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometrically convergent series. The coefficients for these…
This paper investigates the identification of quantiles and quantile regression parameters when observations are set valued. We define the identification set of quantiles of random sets in a way that extends the definition of quantiles for…
In this paper we provide a way to construct new moment sequences from a given moment sequence. An operator based on multivariate positive polynomials is applied to get the new moment sequences. A class of new sequences is corresponding to a…
Word embeddings are effective intermediate representations for capturing semantic regularities between words, when learning the representations of text sequences. We propose to view text classification as a label-word joint embedding…
Consider $N\times N$ hermitian or symmetric random matrices $H$ with independent entries, where the distribution of the $(i,j)$ matrix element is given by the probability measure $\nu_{ij}$ with zero expectation and with variance…