Statistics & Probability Letters最新文献

This paper considers a risk model driven by a spectrally negative Lévy process, where any surplus above $b$ ($0<b<\infty$) is deducted away as dividends and any deficit is covered by injected capitals/raised money. For such a risk model, we define a variant of Parisian ruin time as the first time that the surplus process stays continuously below $a$ ($0<a<b<\infty$) for a time interval with length larger than some pre-specified exponential random variable that is marked on this time interval. A recursive formula for the moments of the Net Present Value (NPV) of dividends paid until Parisian ruin is provided. The expected NPV of capitals injected until the Parisian ruin time is also characterized compactly in terms of the scale functions of the underlying process.

A number of absolute moment-based upper bounds for Gini’s mean difference are extended to general L-moments. Improvement of some bounds by alternative choice of centre for the absolute moments is explored. Different bounds are compared numerically. The distribution for which upper bounds for Gini’s mean difference are attained is given. Extension is made to trimmed L-moments and hence to probability weighted moments.

This work deals with the problem of nonparametric estimation of a regression function when the response variable may be missing according to a not-missing-at-random (NMAR) setup. To assess the theoretical performance of our estimators, we study their strong convergence properties in $L_p$ norms where we also look into their rates of convergence. We also study applications of our results to the problem of statistical classification in semi-supervised learning.

We propose specification tests for parametric quantile regression models versus semiparametric alternatives over a continuum of quantile levels. The test statistics are constructed as continuous functionals of a quantile-marked residual process. We show that using an orthogonal projection on the tangent space of nuisance parameters at each quantile index delivers unified asymptotic properties for tests based on different estimators. Consistency of the tests and asymptotic power under a sequence of local alternatives converging to the null at a parametric rate are also discussed. We propose a simple multiplier bootstrap procedure to carry out the tests, whose nominal levels are well approximated in our simulation study for modest sample sizes.

In the paper, upper bounds for the convergence rate in the limit theorems for random sums of $m$-orthogonal random variables are estimated using the $K$-functional method. Our results are extensions of some known results related to random sums.

Estimating hidden Markov models (HMMs) with unknown number of states is a challenging task. In this paper, we propose a new penalized composite likelihood approach for simultaneously estimating both the number of states and the parameters in an overfitted HMM. We prove the order selection consistency and asymptotic normality of the resultant estimator. Simulation studies and an application demonstrate the finite sample performance of the proposed method.

We prove a Berry–Esseen bound in de Jong’s classical CLT for normalized, completely degenerate $U$-statistics, which says that the convergence of the fourth moment sequence to three and a Lindeberg–Feller type negligibility condition are sufficient for asymptotic normality. Our bound is of the same optimal order as the bound on the Wasserstein distance to normality that has recently been proved by Döbler and Peccati (2017).

The Random Utility Model, central in stochastic choice theory, is equivalent to assume that a probability vector belongs to a convex cone. We investigate its underlying geometry, introduce two new testing procedures, and compare them by simulation.

In this paper, we study the coarse Ricci curvature of inhomogeneous random graph on vertex set $\left[n\right]≔\{1,2,\dots ,n\}$. In this graph, each pair of vertices $(i,j)$ forms an edge independently with probability $\frac{\lambda }{n^{\alpha }}g\left(\frac{i}{n},\frac{j}{n}\right)$ for some function $g(x,y)\in (0,1]$, constants $\lambda >0$ and $\alpha \in [0,1]$. We derive the asymptotic coarse Ricci curvature of this random graph. Phase transition phenomenon exists as $\alpha$ varies from zero to one.

For the discrete Weibull probability distribution we prove that it is only infinitely divisible if the shape parameter lies in the range $0<\beta \le 1$ . The proof is based on some results of Steutel and van Harn (2004). For this case we construct the corresponding compound Poisson distribution and thus the related Lévy process.