Reflection method of estimation for measurement error models

Saqr, Anwar and Khan, Shahjahan (2012) Reflection method of estimation for measurement error models. Journal of Applied Probability and Statistics, 7 (2). pp. 71-88. ISSN 1930-6792

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Abstract

This paper proposes an estimation method based on the reflection of the (manifest) explanatory variable to estimate the parameters of a simple linear regression
model when both response and explanatory variables are subject to measurement error (ME). The reflection method (RM) uses all observed data points, and does not exclude or ignore part of the data or replace them by their ranks. The RM is straightforward, and easy to implement. We show that the RM is equivalent or asymptotically equivalent to the orthogonal regression (OR) method. Simulation studies show that the RM produces estimators that are nearly asymptotically unbiased and efficient under the assumption that the ratio of the error variances equals one. Moreover, it allows to define the sum of squares of errors uniquely, the same way as in the case of no measurement error. Simulation based numerical comparisons of the RM with the ordinary least square (OLS) and OR methods are also included.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Published Version of paper not available, due to publisher copyright restrictions.
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 23 Feb 2013 06:33
Last Modified: 30 Jan 2015 00:56
Uncontrolled Keywords: lLinear regression models; reflection of point; ratio of error variances; orthogonal regression; mean absolute error; method of moments
Fields of Research : 01 Mathematical Sciences > 0104 Statistics > 010401 Applied Statistics
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI: http://eprints.usq.edu.au/id/eprint/22715

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