6 research outputs found
A review on anisotropy analysis of spatial point patterns
A spatial point pattern is called anisotropic if its spatial structure
depends on direction. Several methods for anisotropy analysis have been
introduced in the literature. In this paper, we give an overview of
nonparametric methods for anisotropy analysis of (stationary) point patterns in
and . We discuss methods based on nearest
neighbour and second order summary statistics as well as spectral and wavelet
analysis. All techniques are illustrated on both a clustered and a regular
example. Finally, we discuss methods for testing for isotropy as well as for
estimating preferred directions in a point pattern.Comment: Submitted to Spatial Statistics -journal's special issue of the
Spatial Statistics 2017 conferenc
Consistent estimation in an implicit quadratic measurement error model
An adjusted least squares estimator is derived that yields a consistent estimate of the parameters of an implicit quadratic measurement error model. In addition, a consistent estimator for the measurement error noise variance is proposed. Important assumptions are: (1) all errors are uncorrelated identically distributed and (2) the error distribution is normal. The estimators for the quadratic measurement error model are used to estimate consistently conic sections and ellipsoids. Simulation examples, comparing the adjusted least squares estimator with the ordinary least squares method and the orthogonal regression method, are shown for the ellipsoid fitting problem
On the conic section fitting problem
Adjusted least squares (ALS) estimators for the conic section problem are considered. Consistency of the translation invariant version of ALS estimator is proved. The similarity invariance of the ALS estimator with estimated noise variance is shown. The conditions for consistency of the ALS estimator are relaxed compared with the ones of the paper Kukush et al. [Consistent estimation in an implicit quadratic measurement error model, Comput. Statist. Data Anal. 47(1) (2004) 123–147]
On the conic section fitting problem
Adjusted least squares (ALS) estimators for the conic section problem are considered. Consistency of the translation invariant version of ALS estimator is proved. The similarity invariance of the ALS estimator with estimated noise variance is shown. The conditions for consistency of the ALS estimator are relaxed compared with the ones of the paper Kukush et al. [Consistent estimation in an implicit quadratic measurement error model, Comput. Statist. Data Anal. 47(1) (2004) 123-147].Adjusted least squares Conic fitting Consistent estimator Ellipsoid fitting Quadratic measurement error model