A maximum likelihood estimator of an inhomogeneous Poisson point processes intensity using beta splines

Pavel Krejčíř

Kybernetika (2000)

  • Volume: 36, Issue: 4, page [455]-464
  • ISSN: 0023-5954

Abstract

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The problem of estimating the intensity of a non-stationary Poisson point process arises in many applications. Besides non parametric solutions, e. g. kernel estimators, parametric methods based on maximum likelihood estimation are of interest. In the present paper we have developed an approach in which the parametric function is represented by two-dimensional beta-splines.

How to cite

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Krejčíř, Pavel. "A maximum likelihood estimator of an inhomogeneous Poisson point processes intensity using beta splines." Kybernetika 36.4 (2000): [455]-464. <http://eudml.org/doc/33495>.

@article{Krejčíř2000,
abstract = {The problem of estimating the intensity of a non-stationary Poisson point process arises in many applications. Besides non parametric solutions, e. g. kernel estimators, parametric methods based on maximum likelihood estimation are of interest. In the present paper we have developed an approach in which the parametric function is represented by two-dimensional beta-splines.},
author = {Krejčíř, Pavel},
journal = {Kybernetika},
keywords = {non-stationary Poisson point process; estimating the intensity; non-stationary Poisson point process; estimating the intensity},
language = {eng},
number = {4},
pages = {[455]-464},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A maximum likelihood estimator of an inhomogeneous Poisson point processes intensity using beta splines},
url = {http://eudml.org/doc/33495},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Krejčíř, Pavel
TI - A maximum likelihood estimator of an inhomogeneous Poisson point processes intensity using beta splines
JO - Kybernetika
PY - 2000
PB - Institute of Information Theory and Automation AS CR
VL - 36
IS - 4
SP - [455]
EP - 464
AB - The problem of estimating the intensity of a non-stationary Poisson point process arises in many applications. Besides non parametric solutions, e. g. kernel estimators, parametric methods based on maximum likelihood estimation are of interest. In the present paper we have developed an approach in which the parametric function is represented by two-dimensional beta-splines.
LA - eng
KW - non-stationary Poisson point process; estimating the intensity; non-stationary Poisson point process; estimating the intensity
UR - http://eudml.org/doc/33495
ER -

References

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  3. Daley D. J., Vere–Jones D., An Introduction to the Theory of Point Processes, Springer, New York 1988 Zbl1159.60003MR0950166
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  5. Geyer C. J., Likelihood inference for spatial point processes, In: Stochastic Geometry, Likelihood and Computation (O. E. Barndorff–Nielsen et al, eds.), Chapman and Hall, London 1999, pp. 79–140 (1999) MR1673118
  6. Machek J., On statistical models for the mapping of disease-risk, In: International Conference on Stereology, Spatial Statistics and Stochastic Geometry (V. Beneš, J. Janáček and I. Saxl, eds.), Union of the Czech Mathematicians and Physicists, Prague 1999, pp. 191–196 (1999) 
  7. Marčuk G. I., Methods of Numerical Mathematics, Academia, Prague 1987 MR0931536
  8. Mašata M., Assessment of risk infection by means of a bayesian method, In: International Conference on Stereology, Spatial Statistics and Stochastic Geometry (V. Beneš, J. Janáček and I. Saxl, eds.), Union of the Czech Mathematicians and Physicists, Prague 1999, pp. 197–202 (1999) 
  9. Stern S. H., Cressie N., Inference for extremes in disease mapping, In: Methods of Disease Mapping and Risk Assesment for Public Health Decision Making (A. Lawson et al, eds.), Wiley, New York 1999 Zbl1072.62671
  10. Zeman P., 10.1093/ije/26.5.1121, Internat. J. Epidemiology 26 (1997), 5, 1121–1129 (1997) DOI10.1093/ije/26.5.1121

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