Related papers: Estimating the Upcrossings Index
Under a complex technical condition, similar to such used in extreme value theory, we find the rate q(\epsilon)^{-1} at which a stochastic process with stationary increments \xi should be sampled, for the sampled process \xi(\lfloor\cdot…
We study a special case of the problem of statistical learning without the i.i.d. assumption. Specifically, we suppose a learning method is presented with a sequence of data points, and required to make a prediction (e.g., a classification)…
The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees, Segers and Warchol [Extremes 18(3): 369--402, 2015] proposed estimators of the marginal distributions of this…
The present work investigates two properties of level crossings of a stationary Gaussian process $X(t)$ with autocorrelation function $R_X(\tau)$. We show firstly that if $R_X(\tau)$ admits finite second and fourth derivatives at the…
In this paper, we give sufficient conditions to establish central limit theorems for boundary estimates of Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process.…
We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…
We study the statistics of level spacing of geometric resonances in the disordered binary networks. For a definite concentration $p$ within the interval $[0.2,0.7]$, numerical calculations indicate that the unfolded level spacing…
An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…
A non-homogeneous Poisson cluster model is studied, motivated by insurance applications. The Poisson center process which expresses arrival times of claims, triggers off cluster member processes which correspond to number or amount of…
We consider a bivariate first hitting-time model in which durations are the crossing times of dependent compound Poisson processes with fixed thresholds. The identifiability of the model is discussed, and likelihood estimators of the model…
In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…
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…
This paper considers the problem of adaptive estimation of a non-homogeneous intensity function from the observation of n independent Poisson processes having a common intensity that is randomly shifted for each observed trajectory. We show…
We describe an approach that allows us to deduce the limiting return times distribution for arbitrary sets to be compound Poisson distributed. We establish a relation between the limiting return times distribution and the probability of the…
Understanding the statistics of level crossings in stochastic processes is crucial across many scientific disciplines. The traditional Kac-Rice formula gives the mean rate of level crossings and has found broad use. However, that mean rate…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
In this paper, we deal with the problem of calibrating thresholding rules in the setting of Poisson intensity estimation. By using sharp concentration inequalities, oracle inequalities are derived and we establish the optimality of our…
We introduce a semi-parametric estimator of the Poisson intensity parameter of a spatial stationary Gibbs point process. Under very mild assumptions satisfied by a large class of Gibbs models, we establish its strong consistency and…
We prove that under an easily verifiable set of conditions a sequence of associated random fields converges under rescaling to the Poisson Point Process and give a couple of examples.
There has been considerable recent interest, primarily motivated by problems in applied algebraic topology, in the homology of random simplicial complexes. We consider the scenario in which the vertices of the simplices are the points of a…