The Study On The Unit Level Model With Spatiotemporal Random Effects In Small Area Estimation

Being one of the crucial fields in sample survey, small area estimation, as animportant approach for decision makers to formulate strategies and plan projects, iswidely used in agricultural statistics, Medical Health statistics, social statistics, etc. Atpresent, many scholars pay much attention to researches about space and time seriesmodels in area level, but study on unit level models with spatiotemporal random effectshas been limited.Firstly, we introduce traditional unit level model, space models and time seriesmodels in this paper, and show some existing conclusions in Linear Mixed Model.Secondly, the unit level model with spatiotemporal random effects has been set up, withthe best linear unbiased predictions of the model’s unknown parameters obtained,whose mean-square error estimators upon REML method and ML method have beenderived soon afterwards. Finally, through some related simulations in SAS, we comparethe results of unit level model with spatiotemporal random effects with models onlywith spatial or time effects, as the space and time related coefficients changing. Allresults indicate that with the changing of those coefficients, unit level model withspatiotemporal effects have better results, whose error measure indexes are smaller thanthose of the other two models respectively. Therefore, our model is feasible.