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Estimation in models driven by fractional brownian motion

Corinne Berzin, José R. León (2008)

Annales de l'I.H.P. Probabilités et statistiques

Let {bH(t), t∈ℝ} be the fractional brownian motion with parameter 0<H<1. When 1/2<H, we consider diffusion equations of the type X(t)=c+∫0tσ(X(u)) dbH(u)+∫0tμ(X(u)) du. In different particular models where σ(x)=σ or σ(x)=σ  x and μ(x)=μ or μ(x)=μ  x, we propose a central limit theorem for estimators of H and of σ based on regression methods. Then we give tests of the hypothesis on σ for these models. We also consider functional estimation on σ(⋅)...

Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast

Dia, Galaye, Kone, Abdoulaye (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 60G55; secondary 60G25.We estimate a regression function on a point process by the Tukey regressogram method in a general setting and we give an application in the case of a Risk Process. We show among other things that, in classical Poisson model with parameter r, if W is the amount of the claim with finite espectation E(W) = m, Sn (resp. Rn) the accumulated interval waiting time for successive claims (resp. the aggregate claims amount) up to the...

Estimation of anisotropic gaussian fields through Radon transform

Hermine Biermé, Frédéric Richard (2008)

ESAIM: Probability and Statistics

We estimate the anisotropic index of an anisotropic fractional brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional brownian field and prove that these processes admit...

Estimation of anisotropic Gaussian fields through Radon transform

Hermine Biermé, Frédéric Richard (2007)

ESAIM: Probability and Statistics

We estimate the anisotropic index of an anisotropic fractional Brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional Brownian field and prove that these processes...

Estimation of reduced Palm distributions by random methods for Cox processes with unknown probability law

Emmanuelle Crétois (1995)

Applicationes Mathematicae

Let N i , i ≥ 1, be i.i.d. observable Cox processes on [a,b] directed by random measures Mi. Assume that the probability law of the Mi is completely unknown. Random techniques are developed (we use data from the processes N 1 ,..., N n to construct a partition of [a,b] whose extremities are random) to estimate L(μ,g) = E(exp(-(N(g) - μ(g))) | N - μ ≥ 0).

Estimation of second order parameters using probability weighted moments

Julien Worms, Rym Worms (2012)

ESAIM: Probability and Statistics

The P.O.T. method (Peaks Over Threshold) consists in using the generalized Pareto distribution (GPD) as an approximation for the distribution of excesses over a high threshold. In this work, we use a refinement of this approximation in order to estimate second order parameters of the model using the method of probability-weighted moments (PWM): in particular, this leads to the introduction of a new estimator for the second order parameter ρ, which will be compared to other recent estimators through...

Estimation of second order parameters using probability weighted moments

Julien Worms, Rym Worms (2012)

ESAIM: Probability and Statistics

The P.O.T. method (Peaks Over Threshold) consists in using the generalized Pareto distribution (GPD) as an approximation for the distribution of excesses over a high threshold. In this work, we use a refinement of this approximation in order to estimate second order parameters of the model using the method of probability-weighted moments (PWM): in particular, this leads to the introduction of a new estimator for the second order parameter ρ, which will be compared to other recent estimators through...

Estimation of summary characteristics from replicated spatial point processes

Zbyněk Pawlas (2011)

Kybernetika

Summary characteristics play an important role in the analysis of spatial point processes. We discuss various approaches to estimating summary characteristics from replicated observations of a stationary point process. The estimators are compared with respect to their integrated squared error. Simulations for three basic types of point processes help to indicate the best way of pooling the subwindow estimators. The most appropriate way depends on the particular summary characteristic, edge-correction...

Estimation of the spectral density of a homogeneous random stable discrete time field.

Nicolay N. Demesh, Sergey L. Chekhmenok (2005)

SORT

In earlier papers, 2π-periodic spectral data windows have been used in spectral estimation of discrete- time random fields having finite second-order moments. In this paper, we show that 2π-periodic spectral windows can also be used to construct estimates of the spectral density of a homogeneous symmetric α-stable discrete-time random field. These fields do not have second-order moments if 0 < α < 2. We construct an estimate of the spectrum, calculate the asymptotic mean and variance,...

Estimation of the spectral moment by means of the extrema.

Enrique M. Cabaña (1985)

Trabajos de Estadística e Investigación Operativa

An estimator of the standard deviation of the first derivative of a stationary Gaussian process with known variance and two continuous derivatives, based on the values of the relative maxima and minima, is proposed, and some of its properties are considered.

Estimators of the asymptotic variance of stationary point processes - a comparison

Michaela Prokešová (2011)

Kybernetika

We investigate estimators of the asymptotic variance σ 2 of a d –dimensional stationary point process Ψ which can be observed in convex and compact sampling window W n = n W . Asymptotic variance of Ψ is defined by the asymptotic relation V a r ( Ψ ( W n ) ) ∼ σ 2 | W n | (as n → ∞ ) and its existence is guaranteed whenever the corresponding reduced covariance measure γ red ( 2 ) ( · ) has finite total variation. The three estimators discussed in the paper are the kernel estimator, the estimator based on the second order intesity of the point process and the...

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