On Lehmann's Two-Sample Test

A Kernel Two-Sample Test

We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD). We present two distributionfre...

Least-squares two-sample test

The goal of the two-sample test (a.k.a. the homogeneity test) is, given two sets of samples, to judge whether the probability distributions behind the samples are the same or not. In this paper, we propose a novel non-parametric method of two-sample test based on a least-squares density ratio estimator. Through various experiments, we show that the proposed method overall produces smaller type-...

A Pooled Two-Sample Median Test Based on Density Estimation

Unsupervised Classifier Selection Based on Two-Sample Test

We propose a well-founded method of ranking a pool of m trained classifiers by their suitability for the current input of n instances. It can be used when dynamically selecting a single classifier as well as in weighting the base classifiers in an ensemble. No classifiers are executed during the process. Thus, the n instances, based on which we select the classifier, can as well be unlabeled. T...

Two-Sample Median Test for Vague Data

Classical statistical tests may be sensitive to violations of the fundamental model assumptions inherent in the derivation and construction of these tests. It is obvious that such violations are much more probable in the presence of vague data. Thus nonparametric tests seem to be promising statistical tools. A generalization of the median test for the two-sample problem with vague data is sugge...