Uncited papers are not useless

We study citation dynamics of the papers published in three scientific disciplines (Physics, Economics, and Mathematics) and four broad scientific categories (Medical, Natural, Social Sciences, and Arts & Humanities). We measure the uncitedness ratio, namely, the fraction of uncited papers in these datasets and its dependence on the time following publication. These measurements are compared with the model of citation dynamics which considers acquiring citations as an inhomogeneous Poisson process. The model captures the fraction of uncited papers in our collections fairly well, suggesting that uncitedness is an inevitable consequence of the Poisson statistics. Peer Review https://publons.com/publon/10.1162/qss_a_00142

ESTIMATING THE INTENSITY IN THE FORM OF A POWER FUNCTION OF AN INHOMOGENEOUS POISSON PROCESS

<p>An estimator of the intensity in the form of a power function of an inhomogeneous Poisson process is constructed and investigated. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias, variance and the mean- squared error of the proposed estimator are computed. Asymptotic normality of the estimator is also established.</p>

Misspecified change-point estimation problem for a Poisson process

Consider an inhomogeneous Poisson process X on [0, T] whose unknown intensity function ‘switches' from a lower function g∗ to an upper function h∗ at some unknown point θ∗. What is known are continuous bounding functions g and h such that g∗(t) ≤ g(t) ≤ h(t) ≤ h∗(t) for 0 ≤ t ≤ T. It is shown that on the basis of n observations of the process X the maximum likelihood estimate of θ∗ is consistent for n →∞, and also that converges in law and in pth moment to limits described in terms of the unknown functions g∗ and h∗.

Misspecified change-point estimation problem for a Poisson process

Consider an inhomogeneous Poisson process X on [0, T] whose unknown intensity function ‘switches' from a lower function g∗ to an upper function h∗ at some unknown point θ ∗. What is known are continuous bounding functions g and h such that g∗ (t) ≤ g(t) ≤ h(t) ≤ h∗ (t) for 0 ≤ t ≤ T. It is shown that on the basis of n observations of the process X the maximum likelihood estimate of θ ∗ is consistent for n →∞, and also that converges in law and in pth moment to limits described in terms of the unknown functions g∗ and h ∗.