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

Elena Hadjicosta, Donald Richards

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
JournalMetrika
DOIs
StateAccepted/In press - Jan 1 2019

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Gamma distribution
Integral Transform
Goodness of fit
Test Statistic
Testing
Shape Parameter
Pitman Efficiency
Contiguous Alternatives
Covariance Operator
Power Comparison
Interlacing
Local Alternatives
Hankel transform
Alternatives
Null Distribution
Goodness of Fit Test
Numerical Comparisons
Limiting Distribution
Gaussian Process
Asymptotic distribution

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Integral transform methods in goodness-of-fit testing, I : the gamma distributions. / Hadjicosta, Elena; Richards, Donald.

In: Metrika, 01.01.2019.

Research output: Contribution to journalArticle

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