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Simultaneous prediction using target function based on principal components estimator with correlated errors

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  • Gülesen Üstündağ Şiray

    (Cukurova University)

Abstract

Prediction is pivotal in linear regression analysis, especially in applied sciences. Before target function was defined, the predictions of actual values and/or average values of the dependent variable were obtained individually rather than simultaneously. However, in many applied studies, obtaining simultaneous predictions of both the average values and the actual values is more appropriate. In this paper, the simultaneous prediction based on the principal components estimator with correlated errors in the linear regression model under the problem of multicollinearity, which has negative effects on the prediction, is considered by utilizing the target function. We define three new predictors and make theoretical comparisons of proposed predictors by using the mean squared error of predictions. Also, we support theoretical findings with a comprehensive simulation study and two numerical examples.

Suggested Citation

  • Gülesen Üstündağ Şiray, 2023. "Simultaneous prediction using target function based on principal components estimator with correlated errors," Statistical Papers, Springer, vol. 64(5), pages 1527-1628, October.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:5:d:10.1007_s00362-022-01340-w
    DOI: 10.1007/s00362-022-01340-w
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    References listed on IDEAS

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    1. Trenkler, G., 1984. "On the performance of biased estimators in the linear regression model with correlated or heteroscedastic errors," Journal of Econometrics, Elsevier, vol. 25(1-2), pages 179-190.
    2. Chaturvedi, Anoop & Wan, Alan T. K. & Singh, Shri P., 2002. "Improved Multivariate Prediction in a General Linear Model with an Unknown Error Covariance Matrix," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 166-182, October.
    3. H. Toutenburg & Shalabh, 2002. "Prediction of response values in linear regression models from replicated experiments," Statistical Papers, Springer, vol. 43(3), pages 423-433, July.
    Full references (including those not matched with items on IDEAS)

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