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

Elena Hadjicosta () and Donald Richards ()
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Elena Hadjicosta: Pennsylvania State University
Donald Richards: Pennsylvania State University

Metrika: International Journal for Theoretical and Applied Statistics, 2020, vol. 83, issue 7, No 1, 733-777

Abstract: 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.

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; Primary 33C10; 62G10; Secondary 62G20; 62H15 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00184-019-00749-y

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