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Distribution free goodness of fit testing of grouped Bernoulli trials. (English) Zbl 07101603
Summary: Recently E. Khmaladze [Bernoulli 22, No. 1, 563–588 (2016; Zbl 1345.60094)] has shown how to ‘rotate’ one empirical process to another. We apply this methodology to goodness of fit tests for Bernoulli trials, generated by a single distributional family, but with covariates varying over the sample. Grouping the data, we demonstrate that goodness of fit tests after rotation to distribution free processes are easily computed, and exhibit high power to reject incorrect null hypotheses.
62G10 Nonparametric hypothesis testing
62J12 Generalized linear models (logistic models)
60F05 Central limit and other weak theorems
Full Text: DOI
[1] Khmaladze, E. V., Note on distribution free testing for discrete distributions, Ann. Statist., 41, 2979-2993, (2013) · Zbl 1294.62095
[2] Khmaladze, E. V., Unitary transformations, empirical processes and distribution free testing, Bernoulli, 22, 563-588, (2016) · Zbl 1345.60094
[3] Khmaladze, E. V., Distribution free testing for conditional distributions given covariates, Statist. Probab. Lett., 129, 348-354, (2017) · Zbl 1379.62036
[4] Koul, H. L.; Swordson, E., Khmaladze transformation, (International Encyclopedia of Statistical Science, (2011), Springer), 715-718
[5] Nguyen, T. T.M., Asymptotic Methods of Testing Statistical Hypotheses, (2017), School of Mathematics and Statistics, Victoria University: School of Mathematics and Statistics, Victoria University Wellington, New Zealand, (Ph.D. thesis)
[6] Nguyen, T. T.M., A new approach to distribution free tests in contingency tables, Metrika, 80, 153-170, (2017) · Zbl 1394.62074
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