##### Department of Mathematics,

University of California San Diego

****************************

### Math 295 - Mathematics Colloquium

## Ingird Van Keilegom

#### Universite catholique de Louvain (Belgium)

## Empirical likelihood tests for two-sample problems via nonparametric density estimation

##### Abstract:

We study the problem of testing whether two populations have the same law, by comparing kernel estimators of the two density functions. The proposed test statistic is based on a local empirical likelihood approach. We obtain the asymptotic distribution of the test statistic and propose a bootstrap approximation to calibrate the test. A simulation study is carried out, in which the proposed method is compared with two competitors, and a procedure to select the bandwidth parameter is studied. The proposed test can be extended to more than two samples and to multivariate distributions. (joint work with Ricardo Cao)

Host: A. Delaigle

### January 20, 2005

### 3:00 PM

### AP&M 6438

****************************