The performance of empirical bayes estimates on bootstrap method for poisson gamma models

Abstract

Negative MSE values occured in previous research conducted by Nadhiroh (2009). These might happened due to the nature of jackknife estimators. Jackknife estimators can be negative values under certain scenarios (Bell 2001). The alternative method to estimate the MSE value is required, and this paper proposes bootstrap as an altternative method. To study the consistency of Mean Square Error (MSE) and Average Relative Bias (ARB) on empirical bayes estimators, 2000 bootstrap samples (B) were generated. With B=500 MSE and ARB values seem to achieve consistency and all of MSE values are non negative. This research demonstrated that the Zero Inflated Negative Binomial (ZINB) method is effective in the condition where the excess of zero occurs in small areas. It has been shown that when the probability of zero increases, the smaller MSE values are produced. This research showed that the probabilities of zero affected the ARB means significantly on α=0.05, whereas the number of areas did not effect the ARB means significantly. Although the interaction between probability of zero and number of areas is significant on α=0.05, the mean of MSE decreases as the probability of zero increases with the rate of change the MSE means are different dependent on number of small areas.