Related papers: Confidence disc and square for Cauchy distribution…
The Cauchy distribution is usually presented as a mathematical curiosity, an exception to the Law of Large Numbers, or even as an "Evil" distribution in some introductory courses. It therefore surprised us when Drton and Xiao (2016) proved…
A first systematic study of the effects of the choice of the input scale in global determinations of parton distributions and QCD parameters is presented. It is shown that, although in principle the results should not depend on these…
Concise complexity analyses are presented for simple trust region algorithms for solving unconstrained optimization problems. In contrast to a traditional trust region algorithm, the algorithms considered in this paper require certain…
The method of stable random projections is popular for efficiently computing the Lp distances in high dimension (where 0<p<=2), using small space. Because it adopts nonadaptive linear projections, this method is naturally suitable when the…
Objectives: Estimation of areas under receiver operating characteristic curves (AUCs) and their differences is a key task in diagnostic studies. We aimed to derive, evaluate, and implement simple sample size formulas for such studies with a…
Confidence intervals are an established means of portraying uncertainty about an inferred parameter and can be generated through the use of confidence distributions. For a confidence distribution to be ideal, it must maintain frequentist…
This is the guest editors' general introduction to a Special Issue of the Journal of Statistical Planning and Inference, dedicated to confidence distributions and related themes. Confidence distributions (CDs) are distributions for…
In this series of studies on Cauchy's function $f(z)$ ($z=x+iy$) and its integral $J[f(z)]\equiv (2\pi i)^{-1}\oint_C f(t)dt/(t-z)$ taken along a Jordan contour $C$, the aim is to investigate their comprehensive properties over the entire…
Confidence limits are common place in physics analysis. Great care must be taken in their calculation and use, especially in cases of limited statistics when often one-sided limits are quoted. In order to estimate the stability of the…
In this paper, we consider the Cauchy's problem of global existence and scattering behavior of small, smooth, and localized solutions of cubic fractional Schr\"odinger equations in one dimension, \begin{equation*} \mathrm{i} \partial_t u-…
We employ uncertain parametric CTMCs with parametric transition rates and a prior on the parameter values. The prior encodes uncertainty about the actual transition rates, while the parameters allow dependencies between transition rates.…
Circles of a single size can pack together densely in a hexagonal lattice, but adding in size variety disrupts the order of those packings. We conduct simulations which generate dense random packings of circles with specified size…
In this paper we first provide a method to compute confidence intervals for the center of a piecewise normal distribution given a sample from this distribution, under certain assumptions. We then extend this method to an asymptotic setting,…
In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is to determine two coefficients and multiple parameters (the…
For random matrix models, the parameter estimation based on the traditional likelihood functions is not straightforward in particular when we have only one sample matrix. We introduce a new parameter optimization method for random matrix…
For a singular probability measure $\mu$ on the circle, we show the existence of positive matrices on the unit disc which admit a boundary representation on the unit circle with respect to $\mu$. These positive matrices are constructed in…
In this paper, we begin our discussion with some of the well-known methods available in the literature for the estimation of the parameters of a univariate/multivariate stable distribution. Based on the available methods, a new hybrid…
We introduce a new characterization of the Cauchy distribution and propose a class of goodness-of-fit tests to the Cauchy family. The limit distribution is derived in a Hilbert space framework under the null hypothesis and under fixed…
Post-selection inference consists in providing statistical guarantees, based on a data set, that are robust to a prior model selection step on the same data set. In this paper, we address an instance of the post-selection-inference problem,…
We introduce three notions of multivariate median bias, namely, rectilinear, Tukey, and orthant median bias. Each of these median biases is zero under a suitable notion of multivariate symmetry. We study the coverage probabilities of…