Empirical likelihood based hypothesis testing. (English) Zbl 1015.62048

Einmahl, John H. J.; McKeague, Ian W.

Bernoulli 9, No. 2, 267-290 (2003).

Summary: Omnibus tests for various nonparametric hypotheses are developed using the empirical likelihood method. These include tests for symmetry about zero, changes in distribution, independence and exponentiality. The approach is to localize the empirical likelihood using a suitable ‘time’ variable implicit in the null hypothesis and then form an integral of the log-likelihood ratio statistic. The asymptotic null distributions of these statistics are established. In simulation studies, the proposed statistcs are found to have greater power than corresponding Cramér-von Mises type statistics.

MSC:

62G10

Nonparametric hypothesis testing

Keywords:

change point; distribution-free; exponentially; independence; nonparametric likelihood ratio; symmetry; two-sample problem; exponentiality; simulations