Related papers: Hurst exponent estimation of locally self-similar …

Let X be a second order random process indexed by a compact interval [0,T]. Assume that n independent realizations of X are observed on a fixed grid of p time points. Under mild regularity assumptions on the sample paths of X, we show the…

Using multiple stochastic integrals and the Malliavin calculus, we analyze the asymptotic behavior of quadratic variations for a specific non-Gaussian self-similar process, the Rosenblatt process. We apply our results to the design of…

This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…

We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence…

We present the asymptotic distribution theory for a class of increment-based estimators of the fractal dimension of a random field of the form g{X(t)}, where g:R\to R is an unknown smooth function and X(t) is a real-valued stationary…

In this paper, we establish the Bahadur--Kiefer representation for sample quantiles for a class of weakly dependent linear processes. The rate of approximation is the same as for i.i.d. sequences and is thus optimal.

This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…

We establish the Bahadur representation of sample quantiles for stabilizing score functionals in stochastic geometry and study local fluctuations of the corresponding empirical distribution function. The scores are obtained from a Poisson…

The asymptotic analysis of covariance parameter estimation of Gaussian processes has been subject to intensive investigation. However, this asymptotic analysis is very scarce for non-Gaussian processes. In this paper, we study a class of…

Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94,PF95]. One difficulty in dealing with…

Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal…

The recent accelerated growth in the computing power has generated popularization of experimentation with dynamic computer models in various physical and engineering applications. Despite the extensive statistical research in computer…

The aim of this paper is first the detection of multiple abrupt changes of the long-range dependence (respectively self-similarity, local fractality) parameters from a sample of a Gaussian stationary times series (respectively time series,…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…

The characteristic feature of the discrete scale invariant (DSI) processes is the invariance of their finite dimensional distributions by dilation for certain scaling factor. DSI process with piecewise linear drift and stationary increments…

In this paper, an estimator of $m$ instants ($m$ is known) of abrupt changes of the parameter of long-range dependence or self-similarity is proved to satisfy a limit theorem with an explicit convergence rate for a sample of a Gaussian…

The Hurst exponent is the simplest numerical summary of self-similar long-range dependent stochastic processes. We consider the estimation of Hurst exponent in long-range dependent curve time series. Our estimation method begins by…

A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(\lambda)$ can be written as $f(\lambda)=|\lambda|^{-2d}g(|\lambda|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is…

This paper considers the estimation of quantiles via a smoothed version of the stochastic gradient descent (SGD) algorithm. By smoothing the score function in the conventional SGD quantile algorithm, we achieve monotonicity in the quantile…