Related papers: A simple note on some empirical stochastic process…
In this paper we address the statistical problem of testing if a stationary process is Gaussian. The observation consists in a finite sample path of the process. Using a random projection technique introduced and studied in Cuesta-Albertos…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
Let $\mathcal X=\{\mathcal X_t:\, t\geq0,\, \mathcal X_0=0\}$ be a mean zero $\beta$-stable random walk on $\mathbb{Z}$ with inhomogeneous jump rates $\{\tau_i^{-1}: i\in\mathbb{Z}\}$, with $\beta\in(1,2]$ and $\{\tau_i: i\in\mathbb{Z}\}$ a…
A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…
We present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time. According to the nature of the distribution of time intervals, the probability…
This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures…
We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…
We consider the rate of piecewise constant approximation to a locally stationary process $X(t),t\in [0,1]$, having a variable smoothness index $\alpha(t)$. Assuming that $\alpha(\cdot)$ attains its unique minimum at zero and satisfies the…
Discrete random probability measures are a key ingredient of Bayesian nonparametric inferential procedures. A sample generates ties with positive probability and a fundamental object of both theoretical and applied interest is the…
The goal of this expository article is a fairly self-contained account of some averaging processes of functions along sequences of the form $(\alpha^n x)^{}_{n\in\mathbb{N}}$, where $\alpha$ is a fixed real number with $| \alpha | > 1$ and…
The literature on Bayesian methods for the analysis of discrete-time semi-Markov processes is sparse. In this paper, we introduce the semi-Markov beta-Stacy process, a stochastic process useful for the Bayesian non-parametric analysis of…
We introduce a new measure of robustness for statistical estimators, which we call \emph{empirical sensitivity}. An estimator $\hat \theta$ has bounded empirical sensitivity if, with high probability over a dataset $X = (X_1, \dots, X_n)…
This paper extends Edgeworth-Cornish-Fisher expansions for the distribution and quantiles of nonparametric estimates in two ways. Firstly it allows observations to have different distributions. Secondly it allows the observations to be…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
In a functional setting, we propose two test statistics to highlight the Poisson nature of a Cox process when n copies of the process are available. Our approach involves a comparison of the empirical mean and the empirical variance of the…
We propose a general approach, named by us hyperstatistics, to treat complex systems, in which Boltzmann-Gibbs statistics breaks down in domains of the system. Hyperstatistics preserves the concavity of nonadditive $q$-entropy. We obtain…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
Some special functions are particularly relevant in applied probability and statistics. For example, the incomplete beta function is the cumulative central beta distribution. In this paper, we consider the inversion of the central…
In this paper the estimation of the distribution function for potential outcomes to receiving or not receiving a treatment is studied. The approach is based on weighting observed data on the basis on estimated propensity score. A weighted…
We study the general fragmentation process starting from one element of size unity (E=1). At each elementary step, each existing element of size $E$ can be fragmented into $k\,(\ge 2)$ elements with probability $p_k$. From the continuous…