Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series B, Pt. 1, 84-95

REGRESSION ESTIMATORS UNDER MULTIPLICATIVE MEASUREMENT ERROR SUPERPOPULATION MODELS

By

LORETTA GASCO, HELENO BOLFARINE,

And

MONICA C. SANDOVAL, Universidade de Sao Paulo, Sao Paulo

 

SUMMARY. In this paper we consider prediction of the population total under multiplicative structural and functional measurement error models. Regression type predictors are considered. Two different estimators are considered for the regression coefficient b. The ordinary lest square estimator, which is inconsistent under the multiplicative model and a consistent estimator. The asymptotic distribution of the predictor s considered are investigated and their relative efficiencies derived. As shown, the regression estimator with the ordinary least squares is the one that behaves asymptotically best. Asymptotic results concerning estimators of b are used to prove the main results. A simulation study seems to indicate that this behavior also holds for small sample sizes. Consistent estimators of the predictive variances are also considered.

 

AMS (1991) subject classification. 62D05

Key words and phrases. Super population, regression estimators, multiplicative measurement error models, asymptotics

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