19: Testing for the geometric distribution in multi-sample settings

Music City Center 

This paper deals with simultaneously testing whether k count variables, observed from independent samples, each have geometric laws, where the parameters of these k geometric laws may be different. A test statistic is proposed and shown to be asymptotically distribution free under the null hypothesis, where asymptotic means k→∞. For moderate values of k, this asymptotic null distribution yields conservative tests and so a bootstrap procedure is suggested to approximate the null distribution. Furthermore, this approximation is shown to be consistent. The asymptotic power of the test is also derived, allowing us to determine the alternatives that the new procedure is able to detect. The finite sample performance of the proposal is studied via numerical simulation methods. The test is also applied to the 2024 PGA golf Championship data set. Finally, we observe that the proposed procedure can be imitated to build tests for goodness-of-fit of other distributions in multi-sample settings.

goodness-of-fit

count data

many samples

bootstrap

consistency

asymptotic power 

Section on Nonparametric Statistics