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Integral transform methods in goodness-of-fit testing, I: the gamma distributions

Hadjicosta, E; Richards, D; (2020) Integral transform methods in goodness-of-fit testing, I: the gamma distributions. Metrika , 83 pp. 733-777. 10.1007/s00184-019-00749-y. Green open access

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Abstract

We apply the method of Hankel transforms to develop goodness-of-fit tests for gamma distributions with given shape parameters and unknown rate parameters. We derive the limiting null distribution of the test statistic as an integrated squared Gaussian process, obtain the corresponding covariance operator and oscillation properties of its eigenfunctions, show that the eigenvalues of the operator satisfy an interlacing property, and make applications to two data sets. We prove consistency of the test, provide numerical power comparisons with alternative tests, study the test statistic under several contiguous alternatives, and obtain the asymptotic distribution of the test statistic for gamma alternatives with varying rate or shape parameters and for certain contaminated gamma models. We investigate the approximate Bahadur slope of the test statistic under local alternatives, and we establish the validity of the Wieand condition under which approaches through the approximate Bahadur and the Pitman efficiencies are in accord.

Type: Article
Title: Integral transform methods in goodness-of-fit testing, I: the gamma distributions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00184-019-00749-y
Publisher version: https://doi.org/10.1007/s00184-019-00749-y
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Bahadur slope · Contaminated model · Contiguous alternative · Gaussian process · Generalized Laguerre polynomial · Goodness-of-fit testing · Hankel transform · Hilbert–Schmidt operator · Lipschitz continuity · Modified Bessel function · Pitman efficiency
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics > Clinical Operational Research Unit
URI: https://discovery.ucl.ac.uk/id/eprint/10087842
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