A test for the two-sample problem based on empirical characteristic functions

• Published in: Computational statistics & data analysis Vol. 52; no. 7; pp. 3730 - 3748
• Main Authors: ALBA FERNANDEZ, V, JIMENEZ GAMERO, M. D, GARCIA, J. Munoz
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.03.2008; Elsevier Science; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Distribution theory; Exact sciences and technology; General topics; Mathematics; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Statistical distribution; Sample size; Multivariate analysis; Economic sciences; Hypothesis test; Statistical test; Distribution function; Bootstrap; Jackknife method; Approximation theory; Test power; Sample survey; Data analysis; Approximation; Test statistic; Permutation; Finite sample; Discrete data; Characteristic function; Statistical method; Sampling theory; Statistical computation; Simulation; Weight function; Two sample problem; Econometrics; Resampling method
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2007.12.013

A class of tests for the two sample problem that is based on the empirical characteristic function is investigated. They can be applied to continuous as well as to discrete data of any arbitrary fixed dimension. The tests are consistent against any fixed alternatives for adequate choices of the weight function involved in the definition of the test statistic. Both the bootstrap and the permutation procedures can be employed to estimate consistently the null distribution. The goodness of these approximations and the power of some tests in this class for finite sample sizes are investigated by simulation.