Distribution free goodness of fit testing of grouped Bernoulli trials

Roberts, Leigh

doi:10.1016/j.spl.2019.01.035

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…Adoption of the second transform also appears to be slow. Of the papers Dumitrescu & Khmaladze (2019), Kennedy (2018), Khmaladze (2017), Nguyen (2017a,b) and Roberts (2019), only Kennedy applies the KT2 to real data. He is also the only one of these authors to suggest a wider use of the second KT to choose an optimal model amongst competing models.…”

Section: Introductionmentioning

confidence: 99%

On the derivation of the Khmaladze transforms

Roberts

2021

Preprint

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Some 40 years ago Khmaladze introduced a transform which greatly facilitated the distribution free goodness of fit testing of statistical hypotheses. In the last decade, he has published a related transform, broadly offering an alternative means to the same end.The aim of this paper is to derive these transforms using relatively elementary means, making some simplifications, but losing little in the way of generality. In this way it is hoped to make these transforms more accessible and more widely used in statistical practice. We also propose a change of name of the second transform to the Khmaladze rotation, in order to better reflect its nature.

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Section: Introductionmentioning

confidence: 99%

On the derivation of the Khmaladze transforms

Roberts

2021

Preprint

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“…More specifically, we will construct asymptotically distribution free version of the regression empirical process, so that functionals from this process, used as test statistics, will be asymptotically distribution free. The core of the method is based on the application of unitary operators as described more or less recently in Khmaladze [ , 2016 and studied in Roberts [2019] and Nguyen [2017].…”

Section: Introduction An Illustrative Example With Linear Regressionmentioning

confidence: 99%

Distribution free testing for linear regression. Extension to general parametric regression

Khmaladze¹

2020

Preprint

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Recently a distribution free approach for testing parametric hypotheses based on unitary transformations has been suggested in Khmaladze [ , 2016Khmaladze [ , 2017 and further studied in Nguyen [2017] and Roberts [2019]. In this note we show that the transformation takes extremely simple form in distribution free testing of linear regression. Then we extend it to general parametric regression with vector-valued covariates.

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Distribution-free testing in linear and parametric regression

Khmaladze

2021

Ann Inst Stat Math

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Distribution free goodness of fit testing of grouped Bernoulli trials

Cited by 3 publications

References 6 publications

On the derivation of the Khmaladze transforms

On the derivation of the Khmaladze transforms

Distribution free testing for linear regression. Extension to general parametric regression

Distribution-free testing in linear and parametric regression

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