Survey Methodology
On a new estimator for the variance of the ratio estimator with small sample corrections

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by Paul Knottnerus and Sander ScholtusNote 1

  • Release date: December 17, 2019
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Abstract

The widely used formulas for the variance of the ratio estimator may lead to serious underestimates when the sample size is small; see Sukhatme (1954), Koop (1968), Rao (1969), and Cochran (1977, pages 163-164). In order to solve this classical problem, we propose in this paper new estimators for the variance and the mean square error of the ratio estimator that do not suffer from such a large negative bias. Similar estimation formulas can be derived for alternative ratio estimators as discussed in Tin (1965). We compare three mean square error estimators for the ratio estimator in a simulation study.

Key Words:      Bias; Product moments; Sample variance; Taylor series expansion.

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How to cite

Knottnerus, P., and Scholtus, S. (2019). On a new estimator for the variance of the ratio estimator with small sample corrections. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 45, No. 3. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2019003/article/00003-eng.htm.

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ISSN : 1492-0921

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Survey Methodology publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in survey methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves. All papers will be refereed. However, the authors retain full responsibility for the contents of their papers and opinions expressed are not necessarily those of the Editorial Board or of Statistics Canada.

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Published by authority of the Minister responsible for Statistics Canada.

© Her Majesty the Queen in Right of Canada as represented by the Minister of Industry, 2019

Use of this publication is governed by the Statistics Canada Open Licence Agreement.

Catalogue No. 12-001-X

Frequency: Semi-annual

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. A new variance estimator
Section 3. A simulation study
Section 4. Conclusions
References

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