Abstract
The test statistic of Pearson's Chi-square test for uniformity can be seen as the L 2-distance between the null density and the histogram density estimator. The power of this test depends heavily on the number of histogram cells. Recommended procedures for choosing this number usually exploit the knowledge of the class of alternatives. We present how the Schwarz's Bayesian Information Criterion and certain minimum complexity criteria can be used for selecting the number of classes for Pearson's Chi-square test. These criteria allow us to make a choice depending only on the observed data. We compare the powers of the resulting data driven tests with the power of Chi-square test by means of Monte Carlo simulations. We investigate also a test based on the L 2-distance between the null density and the mixture of histogram density estimators, introduced by J. Rissanen. This test turns out to be much better than Pearson's test, and it is competitive and comparable to other known test procedures.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
