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In different fields of applications including, but not limited to, behavioral, environmental, medical sciences, and econometrics, the use of panel data regression models has become increasingly popular as a general framework for making meaningful statistical inferences. However, when the ordinary least squares (OLS) method is used to estimate the model parameters, presence of outliers may significantly alter the adequacy of such models by producing biased and inefficient estimates. In this work, we propose a new, weighted likelihood based robust estimation procedure for linear panel data models with fixed and random effects. The finite sample performances of the proposed estimators have been illustrated through an extensive simulation study as well as with an application to blood pressure dataset. Our thorough study demonstrates that the proposed estimators show significantly better performances over the traditional methods in the presence of outliers and produce competitive results to the OLS based estimates when no outliers are present in the dataset. 

In many practical applications, spatial data are often collected at areal levels (i.e., block data), and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically depend on integrals of the underlying continuous spatial process. In this paper, we describe a method based onFourier transformsby which multiple integrals of covariance functions over irregular data regions may be numerically approximated with the same level of accuracy as traditional methods, but at a greatly reduced computational expense.