Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
complete statistic; compact sets process; intensity estimation; marked point process; Poisson process; random closed sets; Rao-Blackwell Theorem; segment process; spatial statistic; stochastic geometry; sufficient statistic
complete statistic; compact sets process; intensity estimation; marked point process; Poisson process; random closed sets; Rao-Blackwell Theorem; segment process; spatial statistic; stochastic geometry; sufficient statistic
Summary:
A complete and sufficient statistic is found for stationary marked Poisson processes with a parametric distribution of marks. Then this statistic is used to derive the uniformly best unbiased estimator for the length density of a Poisson or Cox segment process with a parametric primary grain distribution. It is the number of segments with reference point within the sampling window divided by the window volume and multiplied by the uniformly best unbiased estimator of the mean segment length.
References:
[1] Chadoeuf J., Senoussi R., Yao J.F.: Parametric estimation of a Boolean segment process with stochastic restoration estimation. J. Comput. Graphical Statistics 9/2 (2000), 390-402. MR 1823807
[2] Daley D.J., Vere-Jones D.: An Introduction to the Theory of Point Processes. Springer-Verlag New York (1988). MR 0950166 | Zbl 0657.60069
[3] Lehmann E.L.: Theory of Point Estimation. Wadsworth & Brooks California (1991). MR 1143059 | Zbl 0801.62025
[4] Mrkvička T.: Estimation Variances for Poisson Process of Compact Sets. (in Czech), Diploma Thesis, Faculty of Mathematics and Physics, Charles University Prague (1999).
[5] Mrkvička T.: Estimation variances for Poisson Process of Compact Sets. Adv. Appl. Prob. (SGSA) 33 (2001), 765-772. MR 1875778
[6] Stoyan D., Kendall W.S., Mecke J.: Stochastic Geometry and its Applications. John Wiley & Sons Chichester (1995). MR 0895588 | Zbl 0838.60002
Search
Partner of
