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Scandinavian Journal of Statistics
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Article . 2012
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Takacs–Fiksel Method for Stationary Marked Gibbs Point Processes

Takacs-Fiksel method for stationary marked Gibbs point processes
Authors: Coeurjolly, Jean-François; Dereudre, David; Drouilhet, Rémy; Lavancier, Frédéric;

Takacs–Fiksel Method for Stationary Marked Gibbs Point Processes

Abstract

Abstract. This article studies a method to estimate the parameters governing the distribution of a stationary marked Gibbs point process. This procedure, known as the Takacs–Fiksel method, is based on the estimation of the left and right hand sides of the Georgii–Nguyen–Zessin formula and leads to a family of estimators due to the possible choices of test functions. We propose several examples illustrating the interest and flexibility of this procedure. We also provide sufficient conditions based on the model and the test functions to derive asymptotic properties (consistency and asymptotic normality) of the resulting estimator. The different assumptions are discussed for exponential family models and for a large class of test functions. A short simulation study is proposed to assess the correctness of the methodology and the asymptotic results.

Country
France
Keywords

330, central limit theorem, Central limit and other weak theorems, Mathematics - Statistics Theory, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Parametric hypothesis testing, parametric estimation, 510, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Stationary stochastic processes, asymptotic properties, Point processes (e.g., Poisson, Cox, Hawkes processes), stationary marked Gibbs point processes, Takacs-Fiksel method, Asymptotic properties of parametric estimators, ergodic theorem

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
13
Average
Top 10%
Average
Green
bronze