Bussing, Anderson

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Goodness-of-fit testing in two dimensions
(2022-03-02) Bussing, Anderson; Rolke, Wolfgang A.; College of Arts and Sciences - Sciences; Santana Morant, Dámaris; Lorenzo González, Edgardo; Department of Mathematics; Cabrera Rios, Mauricio
A goodness-of-fit (GOF) test is a test used to check whether a sample of data came from a specific probability density. For example, perhaps a particular sample of data looks be evenly distributed across its domain, and one wishes to test if the sample came from a uniform density or not. While many GOF methods are known for univariate data, much less work has been done on multivariate data. In this thesis we will focus specifically on the two-dimensional (bivariate) case. We will provide background on some of the most popular methods, including the famous Chi-square and Kolmogorov-Smirnov tests. We will detail how to calculate the necessary test statistics, and we will provide a variety of power studies to demonstrate each method’s effectiveness in different scenarios. Lastly, we will implement a method of adjusted p-values, where several different goodness-of-fit tests are combined in a particular way to yield a test with high power across all scenarios.