期刊
JOURNAL OF MULTIVARIATE ANALYSIS
卷 165, 期 -, 页码 231-242出版社
ELSEVIER INC
DOI: 10.1016/j.jmva.2017.12.009
关键词
Multivariate goodness-of-fit test; Nearest neighbors; alpha-entropy; Manifold; Test for uniformity on a circle or a sphere; Gamma-ray burst data
资金
- NSF [DMS-1406410]
We present a unified approach to goodness-of-fit testing in R-d and on lower-dimensional manifolds embedded in R-d based on sums of powers of weighted volumes of kth nearest neighbor spheres. We prove asymptotic normality of a class of test statistics under the null hypothesis and under fixed alternatives. Under such alternatives, scaled versions of the test statistics converge to the alpha-entropy between probability distributions. A simulation study shows that the procedures are serious competitors to established goodness-of-fit tests. The tests are applied to two data sets of gamma-ray bursts in astronomy. (C) 2018 Elsevier Inc. All rights reserved.
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