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

Shalabh (), Chandra Mani Paudel () and Narinder Kumar ()
Additional contact information
Shalabh: Indian Institute of Technology, Department of Mathematics and Statistics
Chandra Mani Paudel: Tribhuvan University, Department of Statistics
Narinder Kumar: Panjab University, Department of Statistics

A chapter in Recent Advances in Linear Models and Related Areas, 2008, pp 105-133 from Springer

Abstract: 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.

Keywords: Measurement Error; Target Function; High Order Approximation; Measurement Error Model; Sample Prediction (search for similar items in EconPapers)
Date: 2008
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2064-5_7

Ordering information: This item can be ordered from
http://www.springer.com/9783790820645

DOI: 10.1007/978-3-7908-2064-5_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().