A spatial regression model in a general mixed effects model framework has been proposed for the small area estimation problem. A common autocorrelation parameter across the small areas has resulted in the improvement of the small area estimates. It has been found to be very useful in the cases where there is little improvement in the small area estimates due to the exogenous variables. A second order approximation to the mean squared error (MSE) of the empirical best linear unbiased predictor (EBLUP) has also been worked out. Using the Kalman filtering approach, a spatial temporal model has been proposed. In this case also, a second order approximation to the MSE of the EBLUP has been obtained. As a case study, the time series monthly per capita consumption expenditure (MPCE) data from the National Sample Survey

This paper takes a minimax regression approach to incorporate aversion to parameter uncertainty into the mean-variance model. The uncertainty-averse minimax mean-variance portfolio is obtained by minimizing with respect to the unknown weights the upper bound of the usual quadratic risk function over a fuzzy ellipsoidal set. Beyond the existing approaches, our methodology o¤ers three main advantages: … rst, the resulting optimal portfolio can be interpreted as a Bayesian mean-variance portfolio with the least favorable prior density, and this result allows for a comprehensive comparison with traditional uncertainty-neutral Bayesian mean-variance portfolios. Second, the minimax mean-variance portfolio has a shrinkage expression, but its performance does not necessarily lie within those of the two reference portfolios. Third, we provide closed form ex-pressions for the standard errors of the minimax mean-variance portfolio weights and statistical signi…cance of the optimal portfolio weights can be easily con-ducted. Empirical applications show that incorporating aversion to parameter uncertainty leads to more stable optimal portfolios that outperform traditional uncertainty-neutral Bayesian mean-variance portfolios.

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