On Uncertainty Classes and Minimax Estimation in the Linear Regression Models with Heteroscedasticity and Correlated Errors

The problem of minimax estimation in the linear regression model is considered under the assumption that a prior information about the regression parameter and the covariance matrix of random component (error) is available for the decision-maker. Two models of the uncertainty of the prior knowledge (so called uncertainly classes) are proposed. The first one may represent the problem of estimation for heteroscedastic model, the other may reflect the uncertainty connected with the presence of the correlation among errors. Minimax estimators for considered classes are obtained. Some numerical examples are discussed as well.