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Acta Universitatis Lodziensis. Folia Oeconomica

2004 | 175 Application of Multivariate Statistical Analysis | 107--113
Tytuł artykułu

On Some Robust Against Outliers Predictor of the Total Value in Small Domain

Autorzy
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The problem of prediction of the total value in a domain based on simple regression superpopulation model (with one auxiliary variable and no intercept) is considered. The problem of robust estimation against outliers of regression function's parameter is shown. The presented robust estimator is median value of gradients of all straight lines each determined by the origin and one of n points (x, y), where n is sample size, у - the variable of interest and x - auxiliary variable. This estimator is simplified form of the estimator presented by H. Theil (1979). The equation of the mean square error of the robust predictor based on the robust estimator of regression's parameter is derived for asymptotic assumptions. The best linear predictor based on the considered superpopulation model is presented. The equation of mean square error of the BLU predictor is derived. The accuracy of these predictors is compared for the assumption of normal distribution of variables of interest. (original abstract)
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EN
PL
Rocznik
Strony
107--113
Opis fizyczny
Twórcy
autor
• The Karol Adamiecki University of Economics in Katowice, Poland
autor
• The Karol Adamiecki University of Economics in Katowice, Poland
Bibliografia
• Cassel С. M., Särndal С. Е., Wretman J. Н. (1977), Foundations of Inference in Survey Sampling, John Wiley & Sons, New York-London-Sydney-Toronto.
• Fisz M. (1967), Rachunek prawdopodobieństwa i statystyka matematyczna [in Polish], PWN, Warszawa.
• Royall R. M. (1976), The Linear Least Squares Prediction Approach to Two-Stage Sampling, "Journal of the American Statistical Association", 71, 657-664.
• Theil H. (1979), Zasady ekonometrii [in Polish], PWN, Warszawa.
• Valliant R., Dorfman A. H., Royall R. M. (2000), Finite Population Sampling and Inference. A Prediction Approach, John Wiley & Sons, New York-Chichester-Weinheim-Brisbane-Singapore-Toronto.
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Bibliografia
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