Extended Abstract. Small area estimation has received a lot of attention in recent years due to necessity demand for reliable small area statistics. Direct estimator may not provide adequate precision, because sample size in small areas is seldom large enough. Hence, by employing models that can use auxiliary information and area effects in descriptions, one can increase the precision of direct estimators. Due to more readily available level auxiliary information of area, simplicity and possibility of evaluation of the assumptions used by survey data, area level model has become of comprehensive importance, nowadays. Therefore, basic area level models have been extensively studied in this paper to derive empirical best linear unbiased prediction (EBLUP), empirical Bayes (EB), and hierarchical Bayes (HB) with several different assumptions on parameters. Those models are used to obtion the small area estimators, i.e., the mean of household income in several provinces of Iran, including Khorasan-e-Razavi, Hamedan, Lorsetan, and Tehran. To assess small area estimators, we used 1700 urban households who live in those provinces from the data set of the 2006-2007 Household's Income and Expenditure Survey. Some sampling scheme has been utilized. The optimal total sample size has been more than 400 units, but we have only 212 units available. Due to shortage of sample size, we face large MSE's, encountered us with small area problem.
There are three measures for comparison of small area methods, including average square error (ASE), average absolute of relative bias (AARB), and average of absolute bias (AAB).
We have used two types of transformations, logarithm transformation, and Box-Cox transformation, because of abnormality and heterogeneity of variances.
Our data analysis has shown that it is better to use Box-Cox transformation than to use logarithm transformation, i.e., the test statistic is more significant by using this transformation; but Box-Cox transformation causes large sampling variance, which in some cases results in non-convergence in Gibbs algorithm.
Likewise, HB approach gives better results than EBLUP and EB. All of these approaches are better than direct estimator, i.e., they have smaller values of ASE, AASB, and AAB.