Survey Methodology
Small area quantile estimation via spline regression and empirical likelihood

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by Zhanshou Chen, Jiahua Chen and Qiong ZhangNote 1

  • Release date: May 7, 2019
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Abstract

This paper studies small area quantile estimation under a unit level non-parametric nested-error regression model. We assume the small area specific error distributions satisfy a semi-parametric density ratio model. We fit the non-parametric model via the penalized spline regression method of Opsomer, Claeskens, Ranalli, Kauermann and Breidt (2008). Empirical likelihood is then applied to estimate the parameters in the density ratio model based on the residuals. This leads to natural area-specific estimates of error distributions. A kernel method is then applied to obtain smoothed error distribution estimates. These estimates are then used for quantile estimation in two situations: one is where we only have knowledge of covariate power means at the population level, the other is where we have covariate values of all sample units in the population. Simulation experiments indicate that the proposed methods for small area quantiles estimation work well for quantiles around the median in the first situation, and for a broad range of the quantiles in the second situation. A bootstrap mean square error estimator of the proposed estimators is also investigated. An empirical example based on Canadian income data is included.

Key Words:      Small area quantile; Penalized spline; Empirical likelihood; Density ratio model; Nested-error regression model.

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How to cite

Chen, Z., Chen, J. and Zhang, Q. (2019). Small area quantile estimation via spline regression and empirical likelihood. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 45, No. 1. Paper available at https://www150.statcan.gc.ca/n1/pub/12-001-x/2019001/article/00008-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. Model and assumptions
Section 3. Proposed approach
Section 4. Bootstrap estimation of the mean squared errors
Section 5. Monte Carlo simulations
Section 6. Empirical application
Section 7. Conclusion
Acknowledgements
References

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