Estimation in Elusive Populations Using Multiple Frames and Two-Phase Multiple Frames in the Presence of Measurement and Response Errors

Mutanu Beth; Kahiri James; Odongo Leo

doi:doi:10.11648/j.ajtas.20200905.11

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Estimation in Elusive Populations Using Multiple Frames and Two-Phase Multiple Frames in the Presence of Measurement and Response Errors

Mutanu Beth, Kahiri James, Odongo Leo

Published in American Journal of Theoretical and Applied Statistics (Volume 9, Issue 5)

Received: 4 August 2020 Accepted: 17 August 2020 Published: 8 September 2020

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Abstract

Accurate survey data is important for planning and decision making. The presence of measurement and response errors in surveys has been known to negatively affect the efficiency of estimates as well as to create biases in estimates. It is important to investigate the effects of measurement and response errors when computing survey data so as to obtain reliable information for use by statisticians and policy makers. Unavailability of a sampling frame in a survey for elusive populations has led to the application of multiple frames in sample selection processes. This paper investigates the effect of measurement and response errors in population estimation under multiple and two-phase multiple frames for elusive populations. The effect of random errors and biases from systematic errors on simple and correlated response variances under various levels of multiplicity adjustment factor in multiple frames is carried out. A numerical example is given assuming simple random sampling. The net effect of the errors has been found to inflate simple and correlated response variances and hence overestimation of the variances under different variance estimators. It is therefore recommended that both measurement and response errors be put into consideration when designing and carrying out a survey for more accurate results.

Published in	American Journal of Theoretical and Applied Statistics (Volume 9, Issue 5)
DOI	10.11648/j.ajtas.20200905.11
Page(s)	173-184
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), 2020. Published by Science Publishing Group

Keywords

"Elusive Populations, Multiple Frames, Measurement Errors, Multiple Adjustment Factor, Simple Response Variance, Correlated Response Variance "

References

[1]	Rueda, M. D. M., Arcos, A., Molina, D., & Ranalli, M. G. (2018). Estimation techniques for ordinal data in multiple frame surveys with complex sampling designs. International Statistical Review, 86 (1), 51-67.
[2]	Singh, A. C., Mecatti, F. (2014) Estimation in Multiple Frame Surveys: A simplified and unified review using Multiplicity Approach. Journal of Official Statistics, 155 (4), 51-69.
[3]	del Mar Rueda, M., Ranalli, M. G., Arcos, A., & Molina, D. (2020). Population empirical likelihood estimation in dual frame surveys. Statistical Papers, 1-18.
[4]	Iacan, D., Iachan, R., Dennis, M. L. (1993) A multiple frame approach to sampling the homeless and transient population. Journal of Official Statistics, 9, 747-764.
[5]	Brukelles. (2000) Push and pull factors of international migration, country report: Italy. Technical report 5, Eurostat.
[6]	Singh, A. C., Mecatti, F. (2009) A generalized multiplicity-adjusted Horvitz Thompson class of Multiple frame estimators. Book of Abstract. ITACOSM09, June 10-12/2009, Siena, Italy, Invited paper, 75-77.
[7]	Singh, A. C., Mecatti, F. (2011) Generalized multiplicity-adjusted Horvitz Thompson type Estimation as a unified Approach to Multiple Frame Surveys. Journal of Official Statistics, 27 (4), 633.
[8]	Kalton, G., Anderson, D. W. (1986) Sampling rare populations. Journal of Royal Statistical Society, A, 149 (1), 65-82.
[9]	Lohr, S. L. (2009) Multiple frame survey in sample survey: Design, methods and applications. Handbook of statistics, Pjeffermann, D., Rao, C. R. Eds, 29, A, 71-88.
[10]	Lohr, S. L. (2011) Alternative survey sample desgns : Sampling with multiple overlapping frames. Survey Methodology, 37 (2), 197-213.
[11]	Lohr, S., Rao, J. N. K. (2006) Estimation in multiple frame surveys. Journal of the American Statistical Association, 101 (475), 1019-1030.
[12]	Rao, J. N. K., Wu, C. (2010) Pseudo empirical likelihood inference for multiple frame surveys. Journal of the American Statistical Association, 105 (492), 1494-1503.

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APA Style

Mutanu Beth, Kahiri James, Odongo Leo. (2020). Estimation in Elusive Populations Using Multiple Frames and Two-Phase Multiple Frames in the Presence of Measurement and Response Errors. American Journal of Theoretical and Applied Statistics, 9(5), 173-184. https://doi.org/10.11648/j.ajtas.20200905.11

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ACS Style

Mutanu Beth; Kahiri James; Odongo Leo. Estimation in Elusive Populations Using Multiple Frames and Two-Phase Multiple Frames in the Presence of Measurement and Response Errors. Am. J. Theor. Appl. Stat. 2020, 9(5), 173-184. doi: 10.11648/j.ajtas.20200905.11

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AMA Style

Mutanu Beth, Kahiri James, Odongo Leo. Estimation in Elusive Populations Using Multiple Frames and Two-Phase Multiple Frames in the Presence of Measurement and Response Errors. Am J Theor Appl Stat. 2020;9(5):173-184. doi: 10.11648/j.ajtas.20200905.11

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@article{10.11648/j.ajtas.20200905.11,
  author = {Mutanu Beth and Kahiri James and Odongo Leo},
  title = {Estimation in Elusive Populations Using Multiple Frames and Two-Phase Multiple Frames in the Presence of Measurement and Response Errors},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {5},
  pages = {173-184},
  doi = {10.11648/j.ajtas.20200905.11},
  url = {https://doi.org/10.11648/j.ajtas.20200905.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200905.11},
  abstract = {Accurate survey data is important for planning and decision making. The presence of measurement and response errors in surveys has been known to negatively affect the efficiency of estimates as well as to create biases in estimates. It is important to investigate the effects of measurement and response errors when computing survey data so as to obtain reliable information for use by statisticians and policy makers. Unavailability of a sampling frame in a survey for elusive populations has led to the application of multiple frames in sample selection processes. This paper investigates the effect of measurement and response errors in population estimation under multiple and two-phase multiple frames for elusive populations. The effect of random errors and biases from systematic errors on simple and correlated response variances under various levels of multiplicity adjustment factor in multiple frames is carried out. A numerical example is given assuming simple random sampling. The net effect of the errors has been found to inflate simple and correlated response variances and hence overestimation of the variances under different variance estimators. It is therefore recommended that both measurement and response errors be put into consideration when designing and carrying out a survey for more accurate results.},
 year = {2020}
}

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TY  - JOUR
T1  - Estimation in Elusive Populations Using Multiple Frames and Two-Phase Multiple Frames in the Presence of Measurement and Response Errors
AU  - Mutanu Beth
AU  - Kahiri James
AU  - Odongo Leo
Y1  - 2020/09/08
PY  - 2020
N1  - https://doi.org/10.11648/j.ajtas.20200905.11
DO  - 10.11648/j.ajtas.20200905.11
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  - 173
EP  - 184
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20200905.11
AB  - Accurate survey data is important for planning and decision making. The presence of measurement and response errors in surveys has been known to negatively affect the efficiency of estimates as well as to create biases in estimates. It is important to investigate the effects of measurement and response errors when computing survey data so as to obtain reliable information for use by statisticians and policy makers. Unavailability of a sampling frame in a survey for elusive populations has led to the application of multiple frames in sample selection processes. This paper investigates the effect of measurement and response errors in population estimation under multiple and two-phase multiple frames for elusive populations. The effect of random errors and biases from systematic errors on simple and correlated response variances under various levels of multiplicity adjustment factor in multiple frames is carried out. A numerical example is given assuming simple random sampling. The net effect of the errors has been found to inflate simple and correlated response variances and hence overestimation of the variances under different variance estimators. It is therefore recommended that both measurement and response errors be put into consideration when designing and carrying out a survey for more accurate results.
VL  - 9
IS  - 5
ER  -

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Author Information

Mutanu Beth

Mathematics and Actuarial Science Department, South Eastern Kenya University, Kitui, Kenya
Kahiri James

Mathematics and Actuarial Science Department, Kenyatta University, Nairobi, Kenya
Odongo Leo

Mathematics and Actuarial Science Department, Kenyatta University, Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Mutanu Beth, Kahiri James, Odongo Leo. (2020). Estimation in Elusive Populations Using Multiple Frames and Two-Phase Multiple Frames in the Presence of Measurement and Response Errors. American Journal of Theoretical and Applied Statistics, 9(5), 173-184. https://doi.org/10.11648/j.ajtas.20200905.11

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ACS Style

Mutanu Beth; Kahiri James; Odongo Leo. Estimation in Elusive Populations Using Multiple Frames and Two-Phase Multiple Frames in the Presence of Measurement and Response Errors. Am. J. Theor. Appl. Stat. 2020, 9(5), 173-184. doi: 10.11648/j.ajtas.20200905.11

Copy | Download

AMA Style

Mutanu Beth, Kahiri James, Odongo Leo. Estimation in Elusive Populations Using Multiple Frames and Two-Phase Multiple Frames in the Presence of Measurement and Response Errors. Am J Theor Appl Stat. 2020;9(5):173-184. doi: 10.11648/j.ajtas.20200905.11

Copy | Download

@article{10.11648/j.ajtas.20200905.11,
  author = {Mutanu Beth and Kahiri James and Odongo Leo},
  title = {Estimation in Elusive Populations Using Multiple Frames and Two-Phase Multiple Frames in the Presence of Measurement and Response Errors},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {5},
  pages = {173-184},
  doi = {10.11648/j.ajtas.20200905.11},
  url = {https://doi.org/10.11648/j.ajtas.20200905.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200905.11},
  abstract = {Accurate survey data is important for planning and decision making. The presence of measurement and response errors in surveys has been known to negatively affect the efficiency of estimates as well as to create biases in estimates. It is important to investigate the effects of measurement and response errors when computing survey data so as to obtain reliable information for use by statisticians and policy makers. Unavailability of a sampling frame in a survey for elusive populations has led to the application of multiple frames in sample selection processes. This paper investigates the effect of measurement and response errors in population estimation under multiple and two-phase multiple frames for elusive populations. The effect of random errors and biases from systematic errors on simple and correlated response variances under various levels of multiplicity adjustment factor in multiple frames is carried out. A numerical example is given assuming simple random sampling. The net effect of the errors has been found to inflate simple and correlated response variances and hence overestimation of the variances under different variance estimators. It is therefore recommended that both measurement and response errors be put into consideration when designing and carrying out a survey for more accurate results.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Estimation in Elusive Populations Using Multiple Frames and Two-Phase Multiple Frames in the Presence of Measurement and Response Errors
AU  - Mutanu Beth
AU  - Kahiri James
AU  - Odongo Leo
Y1  - 2020/09/08
PY  - 2020
N1  - https://doi.org/10.11648/j.ajtas.20200905.11
DO  - 10.11648/j.ajtas.20200905.11
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  - 173
EP  - 184
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20200905.11
AB  - Accurate survey data is important for planning and decision making. The presence of measurement and response errors in surveys has been known to negatively affect the efficiency of estimates as well as to create biases in estimates. It is important to investigate the effects of measurement and response errors when computing survey data so as to obtain reliable information for use by statisticians and policy makers. Unavailability of a sampling frame in a survey for elusive populations has led to the application of multiple frames in sample selection processes. This paper investigates the effect of measurement and response errors in population estimation under multiple and two-phase multiple frames for elusive populations. The effect of random errors and biases from systematic errors on simple and correlated response variances under various levels of multiplicity adjustment factor in multiple frames is carried out. A numerical example is given assuming simple random sampling. The net effect of the errors has been found to inflate simple and correlated response variances and hence overestimation of the variances under different variance estimators. It is therefore recommended that both measurement and response errors be put into consideration when designing and carrying out a survey for more accurate results.
VL  - 9
IS  - 5
ER  -

Copy | Download