## Mathematics and Statistics Faculty Publications

#### Title

Empirical Likelihood Ratio Test for Difference of the Means of Zero-inflated Populations

#### Document Type

Article

#### Abstract

Zero-inflated populations characterized by a significant proportion of zero values appear in many applications such as accounting, insurance, medical research, and meteorology. In this article, we consider the problem of testing a difference of the means of two zero-inflated populations. Since zero-inflated populations are highly skewed towards positive values, conventional testing procedures do not perform well and often lead to misleading results. We propose an empirical likelihood ratio test to deal with the problem. The proposed test is derived by jointly specifying the empirical likelihood for the mean parameters and the probability of taking zero value in the data. There are two unique features in this procedure. One is that the information contained in the zero observations is fully utilized and that the proposed test is insensitive to the skewness of the non-zero observations. We derive an asymptotic distribution that will be used to calibrate the statistic in testing the null hypothesis of no mean difference. It is well known that the empirical likelihood method as a non-parametric method does not assume anything about the population distribution beyond certain mild moment conditions, but retains the benefits a parametric likelihood procedure enjoys. It is shown that the proposed empirical likelihood ratio statistic for testing a difference of the means of two zero-inflated populations also has the same asymptotic null distribution as that of the parametric likelihood ratio statistic, namely, a central -distribution. Extensive simulation studies are conducted to assess the performance with small or mediate samples sizes and compared with conventional testing procedures.

#### Repository Citation

Pailden, Junvie and Chen, Hanfeng, "Empirical Likelihood Ratio Test for Difference of the Means of Zero-inflated Populations" (2013). *Mathematics and Statistics Faculty Publications*. 37.

https://scholarworks.bgsu.edu/math_stat_pub/37

#### Publication Date

2013

#### Publication Title

Advances and Applications in Statistics