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Shrinkage Estimation and Prediction for Time Series

For independent samples, shrinkage estimation theory has been developed systematically. Although shrinkage estimators are biased, they improve the MSE of unbiased ones. In view of this, we will develop shrinkage estimation theory and prediction for dependent samples. First, we propose shrinkage estimators for the mean of stationary process and the coefficients of AR model, which improves the MSE of the sample mean and the least squares estimator, respectively. Second, we discuss the problem of shrinkage prediction, and propose a shrinkage predictor which improves the prediction error of the best linear predictor with finite lag length. Third, we will develop the third-order asymptotic theory for shrinked estimators of general curved statistical models, which include time series, multivariate analysis and regression models etc. The results can be applied to portfolio estimation etc. We provide numerical studies, which show some interesting features of shrinkage problems.