Kernel estimation of the diameter distribution in boolean models with spherical grains

DOI10.1080/10485250008832803zbMath0946.62043OpenAlexW2024320134MaRDI QIDQ4485012

Michael Werner, Lothar Heinrich

Publication date: 29 October 2000

Published in: Journal of Nonparametric Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10485250008832803

zbMATH Keywords

asymptotic normalityBoolean modelconvex compact grainspoint process of exposed tangent points

Mathematics Subject Classification ID

Random fields (60G60) Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Geometric probability and stochastic geometry (60D05) Asymptotic properties of parametric tests (62F05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (4)

Statistics for Poisson Models of Overlapping Spheres ⋮ Using two-point set statistics to estimate the diameter distribution in Boolean models with circular grains ⋮ Random Sets: Models and Statistics ⋮ An almost-Markov-type mixing condition and large deviations for Boolean models on the line

Cites Work

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• Asymptotic properties of minimum contrast estimators for parameters of Boolean models
• Estimation of the Size Distribution of Spherical Grains in the Boolean Model
• Estimation of the density in a stationary Boolean model
• Asymptotic Behaviour of an Empirical Nearest-Neighbour Distance Function for Stationary Poisson Cluster Processes
• Asymptotic gaussianity of some estimators for reduced factorial moment measures and product densities of stationary poisson cluster processes
• Asymptotic properties of stereological estimators of volume fraction for stationary random sets
• Asymptotic properties of estimators for parameters of the Boolean model
• Strong convergence of kernel estimators for product densities of absolutely regular point processes
• Statistics of the Boolean model: from the estimation of means to the estimation of distributions

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