Small area estimation with partially linear mixed-t model with measurement error.

In small area estimation (SAE), using direct conventional methods will not lead to reliable estimates because the sample size is small compared to the population. Small Area Estimation under Fay Herriot Model is used to borrow strength from auxiliary variables to improve the effectiveness of a sample size. However, the normality assumption is a limiting assumption for heavy-tailed data and outlying observations. Also, it is usually assumed that the predictors are measured without errors, which can be easily violated in SAE. In this study, we provide a more flexible model beyond these limitations, which is more accurate than the existing models. Specifically, we study SAE in the partially linear mixed-effects model where measurement error is present for the predictors and the vectors of random components and error jointly follow a multivariate t-distribution. Numerical studies are carried out to illustrate the superior performance of the proposed model in the prediction accuracy sense. • Existence of measurement error and non-normal distribution of errors are unavoidable in small area estimation. • Non-linear relationship between covariates and response is usual. • Semi-parametric elliptical linear mixed model can handle all these challenges simultaneously. [ABSTRACT FROM AUTHOR]