Small Area Estimation of Poverty Incidence with Sampling Error Variances Through Generalized Variance Function

Norberto Espejo Milla

doi:doi:10.11648/j.ajtas.20170602.11

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Small Area Estimation of Poverty Incidence with Sampling Error Variances Through Generalized Variance Function

Norberto Espejo Milla

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 2)

Received: 30 December 2016 Accepted: 12 January 2017 Published: 27 February 2017

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Abstract

Small area estimation based on area level models, particularly the EBLUP method, typically assumes that sampling error variances of the direct survey small area estimates are known. In practice, the sampling error variances are unknown. This paper generates EBLUP estimates of poverty incidence when the sampling error variances are estimated using the generalized variance function (GVF) approach. The precision of the EBLUP estimates is determined using a modified version of the Prasad-Rao MSPE estimator. The modification is made by adding an extra term that would account the uncertainty associated with estimating the sampling error variances. The performance of the modified Prasad-Rao estimator relative to the commonly used Prasad-Rao estimator is evaluated through a simulation study. Results have shown that the modified Prasad-Rao MSPE estimator has relatively greater bias than the commonly used Prasad-Rao MSPE estimator, particularly for small samples. A slight gain in precision is observed when using the modified PR MSPE estimator, especially for large samples. Moreover, the findings imply that estimating sampling error variances using GVF models can be a very useful strategy in the application of EBLUP small area estimation, most particularly in poverty incidence estimation.

Published in	American Journal of Theoretical and Applied Statistics (Volume 6, Issue 2)
DOI	10.11648/j.ajtas.20170602.11
Page(s)	72-78
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Small Area Estimation, Generalized Variance Function, Mean Square Prediction Error, Poverty Incidence

References

[1]	Albacea, Z. V. J. (2004). Small area estimation of sub-national poverty incidence. A paper presented at the ADB-GTZ-CEPA Regional Conference on Poverty Monitoring, ADB Headquarters, Manila, Philippines, March 24-26, 2004.
[2]	Bell, W. R. (2008). Examining sensitivity of small area inferences to uncertainty about sampling error variances. Joint Statistical Meetings-Section on Survey Research Methods, 327-334.
[3]	Bogin, B. Caner, A. Choguill, C. L. et al., (2006). Comparison of asset poverty rates to official poverty rates. In Lane, M. V. (Ed.). Trends in poverty and welfare alleviation issues. New York: Nova Science Publishers, Inc.
[4]	Cho, M. J., Eltinge, J. L., Gershunskaya, J., & Huff, L. (2002). Evaluation of generalized variance function estimators for the U.S. current employment survey. Proceedings of the American Statistical Association, Survey Research Methods Section, 534-539.
[5]	Haslett, S. J., Isidro, M. C., & Jones, G. (2010a). Comparison of survey regression techniques in the context of small area estimation of poverty. Survey Methodology 36 (2), 157-170.
[6]	Fay, R. E. and Herriot, R. A. (1979). Estimation of income from small places: An application of James-Stein procedures to census data. Journal of the American Statistical Association, 74 (366): 269–277.
[7]	Haslett, S. J., Isidro, M. C., & Jones, G. (2010). Potential for small area estimation of malnutrition at district and commune level in Cambodia. Survey Methodology 36 (2), 157-170.
[8]	Philippine Statistics Authority (2000). Family income and expenditure survey. Retrieved from https://psa.gov.ph/content/family-income-and-expenditure-survey-fies
[9]	Philippine Statistics Authority (2000). Census of population and housing (CPH). Retrieved from https://psa.gov.ph/content/technical-notes-2000-census-population-and-housing-cph
[10]	Prasad, N. G. N. and Rao, J. N. K. (1990). The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association 85, 163-171.
[11]	Rao, J. N. K. (1999). Some recent advances in model-based small area estimation. Survey Methodology 25, 175-186.
[12]	Rivest, L. P. and Vandal, N. (2003). Mean squared error estimation for small areas when the small area variances are estimated. Proceedings of the International Conference on Recent Advances in Survey Sampling, July 10-13, 2002, Ottawa, Canada.
[13]	Valiant, R. (1987). Generalized variance functions in stratified two-stage sampling. Journal of the American Statistical Association, 82, 499-508.
[14]	Wolter, K. M. (2007). Introduction to variance estimation (2^nd edition). Springer.

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APA Style

Norberto Espejo Milla. (2017). Small Area Estimation of Poverty Incidence with Sampling Error Variances Through Generalized Variance Function. American Journal of Theoretical and Applied Statistics, 6(2), 72-78. https://doi.org/10.11648/j.ajtas.20170602.11

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Norberto Espejo Milla. Small Area Estimation of Poverty Incidence with Sampling Error Variances Through Generalized Variance Function. Am. J. Theor. Appl. Stat. 2017, 6(2), 72-78. doi: 10.11648/j.ajtas.20170602.11

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AMA Style

Norberto Espejo Milla. Small Area Estimation of Poverty Incidence with Sampling Error Variances Through Generalized Variance Function. Am J Theor Appl Stat. 2017;6(2):72-78. doi: 10.11648/j.ajtas.20170602.11

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@article{10.11648/j.ajtas.20170602.11,
  author = {Norberto Espejo Milla},
  title = {Small Area Estimation of Poverty Incidence with Sampling Error Variances Through Generalized Variance Function},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {6},
  number = {2},
  pages = {72-78},
  doi = {10.11648/j.ajtas.20170602.11},
  url = {https://doi.org/10.11648/j.ajtas.20170602.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170602.11},
  abstract = {Small area estimation based on area level models, particularly the EBLUP method, typically assumes that sampling error variances of the direct survey small area estimates are known. In practice, the sampling error variances are unknown. This paper generates EBLUP estimates of poverty incidence when the sampling error variances are estimated using the generalized variance function (GVF) approach. The precision of the EBLUP estimates is determined using a modified version of the Prasad-Rao MSPE estimator. The modification is made by adding an extra term that would account the uncertainty associated with estimating the sampling error variances. The performance of the modified Prasad-Rao estimator relative to the commonly used Prasad-Rao estimator is evaluated through a simulation study. Results have shown that the modified Prasad-Rao MSPE estimator has relatively greater bias than the commonly used Prasad-Rao MSPE estimator, particularly for small samples. A slight gain in precision is observed when using the modified PR MSPE estimator, especially for large samples. Moreover, the findings imply that estimating sampling error variances using GVF models can be a very useful strategy in the application of EBLUP small area estimation, most particularly in poverty incidence estimation.},
 year = {2017}
}

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TY  - JOUR
T1  - Small Area Estimation of Poverty Incidence with Sampling Error Variances Through Generalized Variance Function
AU  - Norberto Espejo Milla
Y1  - 2017/02/27
PY  - 2017
N1  - https://doi.org/10.11648/j.ajtas.20170602.11
DO  - 10.11648/j.ajtas.20170602.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 72
EP  - 78
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20170602.11
AB  - Small area estimation based on area level models, particularly the EBLUP method, typically assumes that sampling error variances of the direct survey small area estimates are known. In practice, the sampling error variances are unknown. This paper generates EBLUP estimates of poverty incidence when the sampling error variances are estimated using the generalized variance function (GVF) approach. The precision of the EBLUP estimates is determined using a modified version of the Prasad-Rao MSPE estimator. The modification is made by adding an extra term that would account the uncertainty associated with estimating the sampling error variances. The performance of the modified Prasad-Rao estimator relative to the commonly used Prasad-Rao estimator is evaluated through a simulation study. Results have shown that the modified Prasad-Rao MSPE estimator has relatively greater bias than the commonly used Prasad-Rao MSPE estimator, particularly for small samples. A slight gain in precision is observed when using the modified PR MSPE estimator, especially for large samples. Moreover, the findings imply that estimating sampling error variances using GVF models can be a very useful strategy in the application of EBLUP small area estimation, most particularly in poverty incidence estimation.
VL  - 6
IS  - 2
ER  -

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Author Information

Norberto Espejo Milla

Department of Statistics, Visayas State University, Baybay City, Philippines

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APA Style

Norberto Espejo Milla. (2017). Small Area Estimation of Poverty Incidence with Sampling Error Variances Through Generalized Variance Function. American Journal of Theoretical and Applied Statistics, 6(2), 72-78. https://doi.org/10.11648/j.ajtas.20170602.11

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ACS Style

Norberto Espejo Milla. Small Area Estimation of Poverty Incidence with Sampling Error Variances Through Generalized Variance Function. Am. J. Theor. Appl. Stat. 2017, 6(2), 72-78. doi: 10.11648/j.ajtas.20170602.11

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AMA Style

Norberto Espejo Milla. Small Area Estimation of Poverty Incidence with Sampling Error Variances Through Generalized Variance Function. Am J Theor Appl Stat. 2017;6(2):72-78. doi: 10.11648/j.ajtas.20170602.11

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@article{10.11648/j.ajtas.20170602.11,
  author = {Norberto Espejo Milla},
  title = {Small Area Estimation of Poverty Incidence with Sampling Error Variances Through Generalized Variance Function},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {6},
  number = {2},
  pages = {72-78},
  doi = {10.11648/j.ajtas.20170602.11},
  url = {https://doi.org/10.11648/j.ajtas.20170602.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170602.11},
  abstract = {Small area estimation based on area level models, particularly the EBLUP method, typically assumes that sampling error variances of the direct survey small area estimates are known. In practice, the sampling error variances are unknown. This paper generates EBLUP estimates of poverty incidence when the sampling error variances are estimated using the generalized variance function (GVF) approach. The precision of the EBLUP estimates is determined using a modified version of the Prasad-Rao MSPE estimator. The modification is made by adding an extra term that would account the uncertainty associated with estimating the sampling error variances. The performance of the modified Prasad-Rao estimator relative to the commonly used Prasad-Rao estimator is evaluated through a simulation study. Results have shown that the modified Prasad-Rao MSPE estimator has relatively greater bias than the commonly used Prasad-Rao MSPE estimator, particularly for small samples. A slight gain in precision is observed when using the modified PR MSPE estimator, especially for large samples. Moreover, the findings imply that estimating sampling error variances using GVF models can be a very useful strategy in the application of EBLUP small area estimation, most particularly in poverty incidence estimation.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Small Area Estimation of Poverty Incidence with Sampling Error Variances Through Generalized Variance Function
AU  - Norberto Espejo Milla
Y1  - 2017/02/27
PY  - 2017
N1  - https://doi.org/10.11648/j.ajtas.20170602.11
DO  - 10.11648/j.ajtas.20170602.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 72
EP  - 78
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20170602.11
AB  - Small area estimation based on area level models, particularly the EBLUP method, typically assumes that sampling error variances of the direct survey small area estimates are known. In practice, the sampling error variances are unknown. This paper generates EBLUP estimates of poverty incidence when the sampling error variances are estimated using the generalized variance function (GVF) approach. The precision of the EBLUP estimates is determined using a modified version of the Prasad-Rao MSPE estimator. The modification is made by adding an extra term that would account the uncertainty associated with estimating the sampling error variances. The performance of the modified Prasad-Rao estimator relative to the commonly used Prasad-Rao estimator is evaluated through a simulation study. Results have shown that the modified Prasad-Rao MSPE estimator has relatively greater bias than the commonly used Prasad-Rao MSPE estimator, particularly for small samples. A slight gain in precision is observed when using the modified PR MSPE estimator, especially for large samples. Moreover, the findings imply that estimating sampling error variances using GVF models can be a very useful strategy in the application of EBLUP small area estimation, most particularly in poverty incidence estimation.
VL  - 6
IS  - 2
ER  -

Copy | Download