Transformed Variables in Survey Sampling
Transformed Variables in Survey Sampling
It can happen, especially in economic surveys, that we are interested in estimating the population mean or total of a variable Y, based on a sample, when a linear model seems appropriate, not for Y itself, but for a strictly monotone transformation of Y. In the present paper, we mainly focus on the important case where the transformation is logarithmic, but some new ideas introduced are not limited to that case. Currently available methods, based on the lognormal distribution, are reviewed, and two new methods introduced, one based on the idea of “smearing” (Duan, 1983), which do not require the lognormal assumption. Theoretical biases and variances are given, with suggestions for sample design and variance estimation, and a practical measure for reducing sensitivity to deviant points is suggested. We evaluate and compare the different estimators we describe in an extensive empirical study based on four economic populations taken from the UK Monthly Wages and Salaries Survey.
Southampton Statistical Sciences Research Institute, University of Southampton
Chambers, Raymond L.
29a4d788-a4f9-4ff4-b6d9-0c0e797c3d56
Dorfman, Alan H.
ee24f795-5a10-4cd5-9457-e74db8fbbccc
2003
Chambers, Raymond L.
29a4d788-a4f9-4ff4-b6d9-0c0e797c3d56
Dorfman, Alan H.
ee24f795-5a10-4cd5-9457-e74db8fbbccc
Chambers, Raymond L. and Dorfman, Alan H.
(2003)
Transformed Variables in Survey Sampling
(S3RI Methodology Working Papers, M03/21)
Southampton, UK.
Southampton Statistical Sciences Research Institute, University of Southampton
41pp.
Record type:
Monograph
(Project Report)
Abstract
It can happen, especially in economic surveys, that we are interested in estimating the population mean or total of a variable Y, based on a sample, when a linear model seems appropriate, not for Y itself, but for a strictly monotone transformation of Y. In the present paper, we mainly focus on the important case where the transformation is logarithmic, but some new ideas introduced are not limited to that case. Currently available methods, based on the lognormal distribution, are reviewed, and two new methods introduced, one based on the idea of “smearing” (Duan, 1983), which do not require the lognormal assumption. Theoretical biases and variances are given, with suggestions for sample design and variance estimation, and a practical measure for reducing sensitivity to deviant points is suggested. We evaluate and compare the different estimators we describe in an extensive empirical study based on four economic populations taken from the UK Monthly Wages and Salaries Survey.
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Published date: 2003
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Local EPrints ID: 8171
URI: http://eprints.soton.ac.uk/id/eprint/8171
PURE UUID: 84a675a5-85e0-4057-8f49-f0715f5033ef
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Date deposited: 11 Jul 2004
Last modified: 15 Mar 2024 04:51
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Contributors
Author:
Raymond L. Chambers
Author:
Alan H. Dorfman
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