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Approximate maximum likelihood estimation for a spatial point pattern.

Jorge Mateu, Francisco Montes (2000)

Qüestiió

Several authors have proposed stochastic and non-stochastic approximations to the maximum likelihood estimate for a spatial point pattern. This approximation is necessary because of the difficulty of evaluating the normalizing constant. However, it appears to be neither a general theory which provides grounds for preferring a particular method, nor any extensive empirical comparisons. In this paper, we review five general methods based on approximations to the maximum likelihood estimate which have...

Approximate polynomial expansion for joint density

D. Pommeret (2005)

Applicationes Mathematicae

Let (X,Y) be a random vector with joint probability measure σ and with margins μ and ν. Let ( P ₙ ) n ∈ ℕ and ( Q ₙ ) n ∈ ℕ be two bases of complete orthonormal polynomials with respect to μ and ν, respectively. Under integrability conditions we have the following polynomial expansion: σ ( d x , d y ) = ∑ n , k ∈ ℕ ϱ n , k P ₙ ( x ) Q k ( y ) μ ( d x ) ν ( d y ) . In this paper we consider the problem of changing the margin μ into μ̃ in this expansion. That is the case when μ is the true (or estimated) margin and μ̃ is its approximation. It is shown that a new joint probability with new margins...

Approximated maximum likelihood estimation of parameters of discrete stable family

Lenka Slámová, Lev B. Klebanov (2014)

Kybernetika

In this article we propose a method of parameters estimation for the class of discrete stable laws. Discrete stable distributions form a discrete analogy to classical stable distributions and share many interesting properties with them such as heavy tails and skewness. Similarly as stable laws discrete stable distributions are defined through characteristic function and do not posses a probability mass function in closed form. This inhibits the use of classical estimation methods such as maximum...

Approximation by Poisson law

Aldona Aleškevičienė, Vytautas Statulevičius (2005)

Discussiones Mathematicae Probability and Statistics

We present here the results of the investigation on approximation by the Poisson law of distributions of sums of random variables in the scheme of series. We give the results pertaining to the behaviour of large deviation probabilities and asymptotic expansions, to the method of cumulants, with the aid of which our results have been obtained.

Approximation of finite-dimensional distributions for integrals driven by α-stable Lévy motion

Aleksander Janicki (1999)

Applicationes Mathematicae

We present a method of numerical approximation for stochastic integrals involving α-stable Lévy motion as an integrator. Constructions of approximate sums are based on the Poissonian series representation of such random measures. The main result gives an estimate of the rate of convergence of finite-dimensional distributions of finite sums approximating such stochastic integrals. Stochastic integrals driven by such measures are of interest in constructions of models for various problems arising...

Approximation of Reliability for a large system with non-markovian repair-times

Jean-Louis Bon, Jean Bretagnolle (2010)

ESAIM: Probability and Statistics

Consider a system of many components with constant failure rate and general repair rate. When all components are reliable and easily reparable, the reliability of the system can be evaluated from the probability q of failure before restoration. In [14], authors give an asymptotic approximation by monotone sequences. In the same framework, we propose, here, a bounding for q and apply it in the ageing property case.

Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet

Laure Coutin, Monique Pontier (2007)

ESAIM: Probability and Statistics

A stochastic “Fubini” lemma and an approximation theorem for integrals on the plane are used to produce a simulation algorithm for an anisotropic fractional Brownian sheet. The convergence rate is given. These results are valuable for any value of the Hurst parameters ( α 1 , α 2 ) ∈ ] 0 , 1 [ 2 , α i ≠ 1 2 . Finally, the approximation process is iterative on the quarter plane ℝ + 2 . A sample of such simulations can be used to test estimators of the parameters αi,i = 1,2.

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