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Uncertainty under a multivariate nested-error regression model with logarithmic transformation

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  • Molina, Isabel

Abstract

This work aims to predict exponentials of mixed effects under a multivariate linear regression model with one random factor. Such quantities are of particular interest in prediction problems where the dependent variable is the logarithm of the variable that is the object of inference. Bias-corrected empirical predictors of the target quantities are defined. A second-order approximation for the mean crossed product error of two of these predictors is obtained, where the mean squared error is a particular case. An estimator of the mean crossed product error with second-order bias is proposed. Finally, results are illustrated through an application related to small area estimation.

Suggested Citation

  • Molina, Isabel, 2009. "Uncertainty under a multivariate nested-error regression model with logarithmic transformation," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 963-980, May.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:5:p:963-980
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    References listed on IDEAS

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    1. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    2. Hsiao, Cheng & Appelbe, Trent W. & Dineen, Christopher R., 1993. "A general framework for panel data models with an application to Canadian customer-dialed long distance telephone service," Journal of Econometrics, Elsevier, vol. 59(1-2), pages 63-86, September.
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    Cited by:

    1. Forough Karlberg, 2015. "Small area estimation for skewed data in the presence of zeroes," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 541-562, December.
    2. Angelo Moretti & Natalie Shlomo & Joseph W. Sakshaug, 2020. "Multivariate Small Area Estimation of Multidimensional Latent Economic Well‐being Indicators," International Statistical Review, International Statistical Institute, vol. 88(1), pages 1-28, April.
    3. Karlberg Forough, 2015. "Small Area Estimation for Skewed Data in the Presence of Zeroes," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 541-562, December.
    4. Forough Karlberg, 2015. "Small Area Estimation For Skewed Data In The Presence Of Zeroes," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 541-562, December.
    5. Angelo Moretti, 2023. "Estimation of small area proportions under a bivariate logistic mixed model," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(4), pages 3663-3684, August.

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