Bootstrap confidence cones for directional data

Given a sample from a distribution F supported on a p-dimensional sphere, several confidence cones for the ‘mean directional vector’ are proposed. Some methods have been available, but they depend on parametric assumptions. In this paper, nonparametric confidence cones based on the bootstrap are con...

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Bibliographic Details
Published in:Biometrika 1985-12, Vol.72 (3), p.637-645
Main Authors: DUCHARME, GILLES R., JHUN, MYOUNGSHIC, ROMANO, JOSEPH P., TRUONG, KINH N.
Format: Article
Language:English
Subjects:
A priori knowledge
Approximation
Bootstrap
Bootstrap resampling
Confidence cone
Consistent estimators
Cumulative distribution functions
Datasets
Directional data
Estimators
Exact sciences and technology
Mathematics
Maximum likelihood estimators
Mean directional vector
Monte Carlo
Nonparametric inference
Probability and statistics
Sample size
Sampling distributions
Sciences and techniques of general use
Statistics
von Mises- Fisher distribution
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Description
Summary:Given a sample from a distribution F supported on a p-dimensional sphere, several confidence cones for the ‘mean directional vector’ are proposed. Some methods have been available, but they depend on parametric assumptions. In this paper, nonparametric confidence cones based on the bootstrap are considered, and consistency of these methods is obtained under minimal conditions. We compare the performances of bootstrap methods with the others by Monte Carlo simulations.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/72.3.637