A COMPARISON OF NONPARAMETRIC ESTIMATORS FOR LENGTH DISTRIBUTION IN LINE SEGMENT PROCESSES

We study nonparametric estimation of the length distribution for stationary line segment processes in the d-dimensional Euclidean space. Several methods have been proposed in the literature. We review different approaches (Horvitz-Thompson type estimator, reduced-sample estimator, Kaplan-Meier estimator, nonparametric maximum likelihood estimator, stochastic restoration estimation) and compare the finite sample behaviour by means of a simulation study for stationary line segment processes in 2D and 3D. Several data generating processes (Poisson point process, Matérn cluster process and Matérn hard-core process II) are considered with both independent and dependent segments. Our finite sample comparison reveals that the nonparametric likelihood estimator provides the most preferable method which works reasonably also if its assumptions are not satisfied.

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Finite Sample Performance of the Empirical Likelihood Estimator under Endogeneity

Computer-Aided Econometrics ◽

10.1201/9780203911570.ch6 ◽

2003 ◽

Author(s):

George Judge ◽

Ron Mittelhammer

Keyword(s):

Empirical Likelihood ◽

Finite Sample ◽

Likelihood Estimator

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Contact and Chord Length Distribution Functions of the Poisson-Voronoi Tessellation in High Dimensions

Advances in Applied Probability ◽

10.1239/aap/1269611143 ◽

2010 ◽

Vol 42 (1) ◽

pp. 48-68 ◽

Cited By ~ 9

Author(s):

L. Muche

Keyword(s):

Voronoi Tessellation ◽

Length Distribution ◽

Distribution Functions ◽

Chord Length ◽

Dimensional Euclidean Space ◽

Spherical Contact ◽

Chord Length Distribution ◽

Special Cases ◽

Contact Distribution ◽

Contact Distribution Function

In this paper we present formulae for contact distributions of a Voronoi tessellation generated by a homogeneous Poisson point process in the d-dimensional Euclidean space. Expressions are given for the probability density functions and moments of the linear and spherical contact distributions. They are double and simple integral formulae, which are tractable for numerical evaluation and for large d. The special cases d = 2 and d = 3 are investigated in detail, while, for d = 3, the moments of the spherical contact distribution function are expressed by standard functions. Also, the closely related chord length distribution functions are considered.

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An Identity for the Nonparametric Maximum Likelihood Estimator in Missing Data and Biased Sampling Models

Bernoulli ◽

10.2307/3318487 ◽

1995 ◽

Vol 1 (4) ◽

pp. 335

Author(s):

Mark J. Van Der Laan

Keyword(s):

Missing Data ◽

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Biased Sampling ◽

Nonparametric Maximum Likelihood ◽

Likelihood Estimator ◽

Nonparametric Maximum Likelihood Estimator

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Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions

Dependence Modeling ◽

10.1515/demo-2019-0021 ◽

2019 ◽

Vol 7 (1) ◽

pp. 394-417

Author(s):

Aboubacrène Ag Ahmad ◽

El Hadji Deme ◽

Aliou Diop ◽

Stéphane Girard

Keyword(s):

Asymptotic Properties ◽

Real Data ◽

Scale Model ◽

Extreme Value Index ◽

Finite Sample ◽

Scale Functions ◽

Nonparametric Estimators ◽

Heavy Tailed Distributions ◽

Finite Sample Properties ◽

Heavy Tailed

AbstractWe introduce a location-scale model for conditional heavy-tailed distributions when the covariate is deterministic. First, nonparametric estimators of the location and scale functions are introduced. Second, an estimator of the conditional extreme-value index is derived. The asymptotic properties of the estimators are established under mild assumptions and their finite sample properties are illustrated both on simulated and real data.

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