Statistics & Probability Letters最新文献

Although the Hawkes process has been widely applied, their probability properties are difficult to obtain, depending on the model structure. This paper proposes a multivariate Hawkes process, which allows for common jumps from each marginal processes. The probability of this common jump is determined by another independent process, which represents the arrival intensity of external shocks to the system. The infinitesimal generator of the new multivariate jump process is derived. Based on that, moments and the Laplace transform are studied, which further demonstrate the advantages of this model structure.

We discuss a representation of any probability distribution on the set of non-negative integers as a waiting time distribution in a sequence of independent Bernoulli trials. Several associated results are derived and illustrated by examples. Multivariate extensions are briefly treated as well.

In this paper, we focus on investigating the asymptotic behavior of solutions in a mean square sense to bilinear Caputo stochastic fractional differential equations (CSFDEs). The main tools in the proof include a variation of the constant formula for CSFDEs, the Jordan normal form of a matrix, the summation formula of Djrbashian type, and constructing a weighted norm in the associated Banach space.

Let $\left(Z_n\right)$ be a supercritical branching process in an independent and identically distributed (i.i.d.) random environment. The paper studies the properties of the estimator $M_n=n^{-1}{\sum }_{k=0}^{n-1}(Z_{k+1}/Z_k)$ introduced by Dion and Esty in 1979. We introduce a related martingale and discuss its convergence and exponential convergence rate. On this basis the exact convergence rate of the central limit theorem for normalized $M_n$ is given.

The win-ratio analysis of controlled clinical trials uses pairwise comparisons between patients in the treatment and control group based on a primary outcome, say time to death, with indeterminacies resolved where possible by a secondary outcome, say time to hospitalization. The resulting preferences may not be transitive. Intransitivity occurs when potential follow-up times vary between patients and rankings from the primary events differ from those from secondary events. We characterize the structure of closed loops, derive some general properties of win-ratio preferences and provide simple numerical illustrations. Under realistic assumptions, unless all potential follow-up times are equal, intransitivities are certain to occur in sufficiently large samples, but their overall frequency is low.

This paper aims to explore the inference of quantile differences using the quantile-based empirical likelihood (QEL) method. In contrast to traditional empirical likelihood-based approaches, the proposed method yields an explicit likelihood ratio, making it user-friendly in practical applications. Additionally, as an expansion, the comparison of quantile differences between two populations is initially considered as a measure of differences. The limiting distribution of the smoothed log-empirical likelihood ratio for both cases is theoretically derived. The paper also includes simulation studies and an analysis of a dataset comprising 6033 genes.

In this note we explore how standard statistical distances are equivalent for discrete log-concave distributions. Distances include total variation distance, Wasserstein distance, and $f$-divergences.

This paper presents a weighted efficiency optimality criterion to obtain a compound optimal design that balances two different optimality objectives. An equivalence theorem and a search algorithm for a concave–concave combination of criteria for finding the weighted efficiency optimal design are given and applied to the Scheffé mixture model.

Let ${\left\{V_t\right\}}_{t=1}^n$ be any univariate stationary first-order semiparametric Markov process generated from an unknown invariant marginal distribution and a bivariate Gaussian copula with unknown correlation coefficient ${\alpha }_0\in (-1,1)$. We prove that $\left(1-{\alpha }_0^2\right)$ is the semiparametric efficient variance bound for estimating the correlation parameter ${\alpha }_0$ in any Gaussian copula generated first-order stationary Markov models. Surprisingly, this variance bound is strictly larger than ${\left(1-{\alpha }_0^2\right)}^2$ (when ${\alpha }_0\ne 0$), which is the semiparametric efficient variance bound derived by Klaassen and Wellner (1997) for estimating the correlation parameter using any $i.i.d.$ data ${\left\{(X_i,Y_i)\right\}}_{i=1}^n$ generated from a bivariate Gaussian copula with two unknown marginal distributions.