Simultaneous Prediction of Actual and Average Values of Response Variable in Replicated Measurement Error Models

Prediction is an important aspect of decision-making process through statistical methodology. Linear regression modeling plays an important role in the prediction of an unknown value of study variable corresponding to a known value of explanatory variable. Usually, when the least square estimators are used to construct the predictors, they yield the best linear unbiased predictors provided the data recorded on variables is measured without any error. In practice, many applications fail to meet the assumption of error free observations due to various reasons. for example, due to indirect measurements, practical difficulties, qualitative variables and proxy measurements etc., the measurement error is induced in the data. The usual statistical tools in the context of linear regression analysis like ordinary least squares method then yields biased and inconsistent estimators, see Cheng and Van Ness (1999), Fuller (1987) for more details. Consequently, the predictors obtained through these estimators also then become invalid. Construction of good predictors for measurement error-ridden data and study of their performance properties under measurement error models is attempted in this article.

The organization of this article is as follows. In next Section 2, we discuss the model and the target function of prediction. The predictors are constructed and discussed in Section 3. In Section 4, we derive and analyze the large sample asymptotic performance properties of the predictors in within and outside sample prediction cases. A Monte- Carlo simulation experiment is conducted to study the performance properties of the predictors in finite sample and its findings are reported in Section 5. Some concluding remarks are given in Section 6. The derivations of the results are given in Section 7.