Direct estimators of parameters are not precise because of little surveys unit in Small Areas. Regarding the wide spread increase of demand for providing valid and accurate statistics for Small Areas, attempts have been made to present proper solutions for the problems. Small Area Estimation approaches provide the direct estimators with borrowing strength to increase their precision based on a model, especially about those estimators that are based on the linear mixed model including random Area effects and using various auxiliary sources. Data associated with spatially contiguous Small Areas may be modeled via covariates, with error terms that are spatially dependent according to neighbor Areas. In this paper we investigate Small Area Estimation based on linear models with spatially correlated Small Area effects where the neighborhood structure is described by a contiguity matrix. Such models allow efficient use of spatial auxiliary information in Small Area Estimation. Then Estimation for Small Areas will be achieved for the amount of agronomy production in Fars province, according to the two common EBLUP and MBDE methods and two usual (non spatial) and spatial approaches based on the unit level model. Then the accuracy of them have been compared.

Small Area Estimation has received a lot of attention in recent years due to growing demand for reliable Small Area statistics. Traditional Area-specific estimators may not provide adequate precision because sample sizes in Small Areas are seldom large enough. This makes it necessary to employ indirect estimators based on linking models. Basic Area level and unit level models have been extensively studied in the literature to derive empirical best linear unbiased prediction (EBLUP), empirical Bayes (EB) and hierarchical Bayes (HB) Small Area estimators and associated measures of variability. In this paper, I will cover several important new developments related to model-based Small Area Estimation.  

Small Area Estimation methods have been considered in various fields, especially medicine, agriculture, economics, social sciences, and political Science. These methods have many applications in providing reliable statistics for Small-sample or non-sample statistical Areas. In estimating the Small Area, there are two approaches: the basic design and the basic model. In this paper, a model-based approach to labor force indicators is considered using a multinomial mixed Logit model. The practical application of the method proposed in this article is to estimate the total number of employees, unemployed and unemployment rate using household income and expenditure data for Semnan province by cities; Semnan, Shahroud, Damghan and Garmsar concerning the period 2011-2016. Finally, we have found the estimates of unemployment rate for Garmsar (9.14), Semnan (9.84), Damghan (11.29), and Shahroud (12.40) in 2016. The more distance from Tehran (the Iranian Capital), the more is the unemployment rate!

The most widely used model in Small Area Estimation is the Area level or the Fay-Herriot model. In this model, it is typically assumed that both the Area level random effects (model errors) and the sampling errors have a Gaussian distribution. However, considerable variations in error components (model errors and sampling errors) can cause poor performance in Small Area Estimation. In this paper, to overcome this problem, the symmetric ,-stable distribution is used to deal with outliers in the error components. The model parameters are estimated with the empirical Bayes method. The performance of the proposed model is investigated in different simulation scenarios and compared with the existing classic and robust empirical Bayes methods. The proposed model can improve Estimation results, in particular when both error components are normal or have heavy-tailed distribution.

The boosting algorithm is a hybrid algorithm to reduce variance, a family of machine learning algorithms in supervised learning. This algorithm is a method to transform weak learning systems into strong systems based on the combination of different results. In this paper, mixture models with random effects are considered for Small Areas, where the errors follow the AR-GARCH model. To select the variable, machine learning algorithms, such as boosting algorithms, have been proposed. Using simulated and tax liability data, the boosting algorithm's performance is studied and compared with classical variable selection methods, such as the step-by-step method.

Background: Adolescence is one of the most important periods in the course of human evolution and the prevalence of mental disorders among adolescence in different regions of Iran, especially in southern Iran.Objectives: This study was conducted to determine the prevalence of mental disorders among high school students in Bushehr province, south of Iran.Methods: In this cross-sectional study, 286 high school students were recruited by a multi-stage random sampling in Bushehr province in 2015. A general health questionnaire (GHQ-28) was used to assess mental disorders. The Small Area method, under the hierarchical Bayesian approach, was used to determine the prevalence of mental disorders and data analysis.Results: From 286 questionnaires only 182 were completely filed and evaluated (the response rate was 70.5%). Of the students, 58.79% and 41.21% were male and female, respectively. Of all students, the prevalence of mental disorders in Bushehr, Dayyer, Deylam, Kangan, Dashtestan, Tangestan, Genaveh, and Dashty were 0.48, 0.42, 0.45, 0.52, 0.41, 0.47, 0.42, and 0.43, respectively.Conclusions: Based on this study, the prevalence of mental disorders among adolescents was increasing in Bushehr Province counties. The lack of a national policy in this way is a serious obstacle to mental health and wellbeing access.