Calibration Estimators for Population Mean with Subsampling the Nonrespondents Under Stratified Sampling

Iseh Matthew Joshua; Bassey Mbuotidem Okon

doi:doi:10.11648/j.sjams.20221004.11

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Calibration Estimators for Population Mean with Subsampling the Nonrespondents Under Stratified Sampling

Iseh Matthew Joshua, Bassey Mbuotidem Okon

Published in Science Journal of Applied Mathematics and Statistics (Volume 10, Issue 4)

Received: 7 August 2022 Accepted: 27 August 2022 Published: 16 September 2022

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Abstract

The existence of nonresponse in survey sampling has engendered inconsistencies in the estimation of population parameter. Such estimation, being characterized by nonresponse bias has become a rule rather than the exception in survey sampling, and this has been long acknowledged in the literature. Several authors have come up with different techniques such as subsampling the nonresponse, imputation, and calibration to curb this menace. An attempt to overcome the challenges faced in existing works, this study considered the estimation of finite population mean using calibration approach with subsampling the nonrespondents. Owning to the fact that calibration estimation has been found to reduce bias and improve efficiency of estimators. The classical estimator by Hansen and Hurwitz for estimating the population mean with subsampling the nonrespondents is calibrated upon using the chi square distance function, and different choices of the tunning parameter result in the calibration estimators of combined regression and ratio. Expressions for the bias, variance and mean square error (MSE) of the proposed estimators are derived and their properties studied. Again, the optimum conditions under which the suggested estimators have minimum variance and MSE are equally provided. Both efficiency and empirical comparisons are in favor of the proposed estimators, and suggest that the proposed estimators are more efficient and reliable with high precision than the existing estimators even in double sampling. In addition, expressions for optimal sample sizes with respect to the cost of the survey have been derived to validate the superiority of the proposed estimators, and the empirical investigation confirms the proposed estimators as highly preferable.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 10, Issue 4)
DOI	10.11648/j.sjams.20221004.11
Page(s)	45-56
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

Auxiliary Variable, Calibration, Nonresponse, Stratified Sampling, Sub-sampling

References

[1]	M. H. Hansen and N. W. Hurwitz, “The problem of non-response in sample surveys”, J. Amer. Statist. Assoc., 41, 517-529, (1946).
[2]	K. M. Chaudhary, R. Singh, R. K. Shukla and M. Kumar, “A family of estimators for estimating population mean in Stratified sampling under nonresponse”, Pakistan Journal of Statistics and Operations Research, 5 (1), 47-54, (2009).
[3]	K. M. Chaudhary, V. K. Singh and R. K. Shukla, “Combined-type family of estimators of population mean in stratified random sampling under nonresponse”, Journal of Reliability and Statistical studies (JRSS), 5 (2), 133-142, (2012).
[4]	S. Kumar, “Efficient use of auxiliary information in estimating the population ratio, product and mean in the presence of non-response”, Journal for Advanced Computing. 4, 68-87, (2015).
[5]	K. M. Chaudhary and A. Kumar, “Use of double sample scheme in estimating the mean of stratified population under non-response”, STATISTICA, anno, LXXV, n. 4 (2015).
[6]	A. Sanaullah, I. Elisan and M. Noor-UI-Amin, “Estimation of mean for a finite population using subsampling of nonrespondents”, Journal of Statistics and Management Systems, 22 (6), 1015-1035, (2019).
[7]	G. N. Singh and M. Usman, “Improved regression cum ratio estimators using information on two auxiliary variables dealing with subsampling technique of nonresponse”, Journal of Statistical Theory and Practice, 14 (1), 1-28, (2020).
[8]	N. Garib and U. Mahamood, “Enhanced estimation of population distribution function in the presence of non-response”, http://dio.org/10.1016/,asej. 2021.02.002.
[9]	A. E. Anieting and E. I. Enang, “Two-Phase stratified sampling Estimator for population mean in the presence of nonresponse using one auxiliary variable”, Math. J. Interdiscip. Sci. 8 (2), 49-56, (2020).
[10]	A. E. Anieting, E. I. Enang and C. E. Onwukwe, “Efficient estimator for Population mean in stratified double sampling in the presence of nonresponse using one auxiliary variable”, African Journal of Mathematics and Statistical Studies 4 (2), 40-50, (2021). DOI: 10525589/AJMSS-YF4VIIQV.
[11]	S. Guha and H. Chandra, “Improved estimation of finite population mean in two-phase sampling with subsampling of the nonrespondents”, Mathematical Population Studies 28 (1), 24-44, (2020).
[12]	M. K Chaudhary, A. Kumar, and G. K. Vishwarkarma, “Some improved estimators of population mean using two-phase sampling scheme in the presence of nonresponse”, Pakistan Journal of Statistics and Operations Research, 17 (4), 911-919, (2021). DOI: 10.18187/Pjsor.v17i4.2505.
[13]	M. J. Iseh and K. J. Bassey, “Calibration estimator for population mean in small sample size with nonresponse”, European Journal of Statistics and Probability, 9 (1), 32-42, (2021a).
[14]	M. J. Iseh and K. J. Bassey, “A new calibration estimator of population mean for small area with nonresponse” Asian Journal of Probability and Statistics. 12 (2), 41-51, (2021b). DOI: 10.9734/AJPAS/2021/v12i230286.
[15]	J. C. Deville and C. E. Sarndal, “Calibration estimators in survey sampling’, Journal of the American Statistical Association, 87, 376-382. (1992).
[16]	M. J. Iseh, and E. I. Enang, “A Calibration Synthetic Estimator of population Mean in Small Area under Stratified Sampling Design”, Transition in Statistics new series, 22 (3), 15-30, (2021). DOI: 10.21307/stattrans-2021-025.
[17]	N. Koyuncu, and C. Kadilar, “Family of estimators of population mean using two auxiliary variables in stratified random sampling”, Communication in Statistics Theory and Methods, 38 (14), 2398-2417.

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APA Style

Iseh Matthew Joshua, Bassey Mbuotidem Okon. (2022). Calibration Estimators for Population Mean with Subsampling the Nonrespondents Under Stratified Sampling. Science Journal of Applied Mathematics and Statistics, 10(4), 45-56. https://doi.org/10.11648/j.sjams.20221004.11

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ACS Style

Iseh Matthew Joshua; Bassey Mbuotidem Okon. Calibration Estimators for Population Mean with Subsampling the Nonrespondents Under Stratified Sampling. Sci. J. Appl. Math. Stat. 2022, 10(4), 45-56. doi: 10.11648/j.sjams.20221004.11

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AMA Style

Iseh Matthew Joshua, Bassey Mbuotidem Okon. Calibration Estimators for Population Mean with Subsampling the Nonrespondents Under Stratified Sampling. Sci J Appl Math Stat. 2022;10(4):45-56. doi: 10.11648/j.sjams.20221004.11

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@article{10.11648/j.sjams.20221004.11,
  author = {Iseh Matthew Joshua and Bassey Mbuotidem Okon},
  title = {Calibration Estimators for Population Mean with Subsampling the Nonrespondents Under Stratified Sampling},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {10},
  number = {4},
  pages = {45-56},
  doi = {10.11648/j.sjams.20221004.11},
  url = {https://doi.org/10.11648/j.sjams.20221004.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20221004.11},
  abstract = {The existence of nonresponse in survey sampling has engendered inconsistencies in the estimation of population parameter. Such estimation, being characterized by nonresponse bias has become a rule rather than the exception in survey sampling, and this has been long acknowledged in the literature. Several authors have come up with different techniques such as subsampling the nonresponse, imputation, and calibration to curb this menace. An attempt to overcome the challenges faced in existing works, this study considered the estimation of finite population mean using calibration approach with subsampling the nonrespondents. Owning to the fact that calibration estimation has been found to reduce bias and improve efficiency of estimators. The classical estimator by Hansen and Hurwitz for estimating the population mean with subsampling the nonrespondents is calibrated upon using the chi square distance function, and different choices of the tunning parameter result in the calibration estimators of combined regression and ratio. Expressions for the bias, variance and mean square error (MSE) of the proposed estimators are derived and their properties studied. Again, the optimum conditions under which the suggested estimators have minimum variance and MSE are equally provided. Both efficiency and empirical comparisons are in favor of the proposed estimators, and suggest that the proposed estimators are more efficient and reliable with high precision than the existing estimators even in double sampling. In addition, expressions for optimal sample sizes with respect to the cost of the survey have been derived to validate the superiority of the proposed estimators, and the empirical investigation confirms the proposed estimators as highly preferable.},
 year = {2022}
}

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TY  - JOUR
T1  - Calibration Estimators for Population Mean with Subsampling the Nonrespondents Under Stratified Sampling
AU  - Iseh Matthew Joshua
AU  - Bassey Mbuotidem Okon
Y1  - 2022/09/16
PY  - 2022
N1  - https://doi.org/10.11648/j.sjams.20221004.11
DO  - 10.11648/j.sjams.20221004.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 45
EP  - 56
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20221004.11
AB  - The existence of nonresponse in survey sampling has engendered inconsistencies in the estimation of population parameter. Such estimation, being characterized by nonresponse bias has become a rule rather than the exception in survey sampling, and this has been long acknowledged in the literature. Several authors have come up with different techniques such as subsampling the nonresponse, imputation, and calibration to curb this menace. An attempt to overcome the challenges faced in existing works, this study considered the estimation of finite population mean using calibration approach with subsampling the nonrespondents. Owning to the fact that calibration estimation has been found to reduce bias and improve efficiency of estimators. The classical estimator by Hansen and Hurwitz for estimating the population mean with subsampling the nonrespondents is calibrated upon using the chi square distance function, and different choices of the tunning parameter result in the calibration estimators of combined regression and ratio. Expressions for the bias, variance and mean square error (MSE) of the proposed estimators are derived and their properties studied. Again, the optimum conditions under which the suggested estimators have minimum variance and MSE are equally provided. Both efficiency and empirical comparisons are in favor of the proposed estimators, and suggest that the proposed estimators are more efficient and reliable with high precision than the existing estimators even in double sampling. In addition, expressions for optimal sample sizes with respect to the cost of the survey have been derived to validate the superiority of the proposed estimators, and the empirical investigation confirms the proposed estimators as highly preferable.
VL  - 10
IS  - 4
ER  -

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Author Information

Iseh Matthew Joshua

Department of Statistics, Akwa Ibom State University, Mkpat Enin, Nigeria
Bassey Mbuotidem Okon

Department of Statistics, Akwa Ibom State University, Mkpat Enin, Nigeria

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Plain Text BibTeX RIS

APA Style

Iseh Matthew Joshua, Bassey Mbuotidem Okon. (2022). Calibration Estimators for Population Mean with Subsampling the Nonrespondents Under Stratified Sampling. Science Journal of Applied Mathematics and Statistics, 10(4), 45-56. https://doi.org/10.11648/j.sjams.20221004.11

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ACS Style

Iseh Matthew Joshua; Bassey Mbuotidem Okon. Calibration Estimators for Population Mean with Subsampling the Nonrespondents Under Stratified Sampling. Sci. J. Appl. Math. Stat. 2022, 10(4), 45-56. doi: 10.11648/j.sjams.20221004.11

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AMA Style

Iseh Matthew Joshua, Bassey Mbuotidem Okon. Calibration Estimators for Population Mean with Subsampling the Nonrespondents Under Stratified Sampling. Sci J Appl Math Stat. 2022;10(4):45-56. doi: 10.11648/j.sjams.20221004.11

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@article{10.11648/j.sjams.20221004.11,
  author = {Iseh Matthew Joshua and Bassey Mbuotidem Okon},
  title = {Calibration Estimators for Population Mean with Subsampling the Nonrespondents Under Stratified Sampling},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {10},
  number = {4},
  pages = {45-56},
  doi = {10.11648/j.sjams.20221004.11},
  url = {https://doi.org/10.11648/j.sjams.20221004.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20221004.11},
  abstract = {The existence of nonresponse in survey sampling has engendered inconsistencies in the estimation of population parameter. Such estimation, being characterized by nonresponse bias has become a rule rather than the exception in survey sampling, and this has been long acknowledged in the literature. Several authors have come up with different techniques such as subsampling the nonresponse, imputation, and calibration to curb this menace. An attempt to overcome the challenges faced in existing works, this study considered the estimation of finite population mean using calibration approach with subsampling the nonrespondents. Owning to the fact that calibration estimation has been found to reduce bias and improve efficiency of estimators. The classical estimator by Hansen and Hurwitz for estimating the population mean with subsampling the nonrespondents is calibrated upon using the chi square distance function, and different choices of the tunning parameter result in the calibration estimators of combined regression and ratio. Expressions for the bias, variance and mean square error (MSE) of the proposed estimators are derived and their properties studied. Again, the optimum conditions under which the suggested estimators have minimum variance and MSE are equally provided. Both efficiency and empirical comparisons are in favor of the proposed estimators, and suggest that the proposed estimators are more efficient and reliable with high precision than the existing estimators even in double sampling. In addition, expressions for optimal sample sizes with respect to the cost of the survey have been derived to validate the superiority of the proposed estimators, and the empirical investigation confirms the proposed estimators as highly preferable.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Calibration Estimators for Population Mean with Subsampling the Nonrespondents Under Stratified Sampling
AU  - Iseh Matthew Joshua
AU  - Bassey Mbuotidem Okon
Y1  - 2022/09/16
PY  - 2022
N1  - https://doi.org/10.11648/j.sjams.20221004.11
DO  - 10.11648/j.sjams.20221004.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 45
EP  - 56
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20221004.11
AB  - The existence of nonresponse in survey sampling has engendered inconsistencies in the estimation of population parameter. Such estimation, being characterized by nonresponse bias has become a rule rather than the exception in survey sampling, and this has been long acknowledged in the literature. Several authors have come up with different techniques such as subsampling the nonresponse, imputation, and calibration to curb this menace. An attempt to overcome the challenges faced in existing works, this study considered the estimation of finite population mean using calibration approach with subsampling the nonrespondents. Owning to the fact that calibration estimation has been found to reduce bias and improve efficiency of estimators. The classical estimator by Hansen and Hurwitz for estimating the population mean with subsampling the nonrespondents is calibrated upon using the chi square distance function, and different choices of the tunning parameter result in the calibration estimators of combined regression and ratio. Expressions for the bias, variance and mean square error (MSE) of the proposed estimators are derived and their properties studied. Again, the optimum conditions under which the suggested estimators have minimum variance and MSE are equally provided. Both efficiency and empirical comparisons are in favor of the proposed estimators, and suggest that the proposed estimators are more efficient and reliable with high precision than the existing estimators even in double sampling. In addition, expressions for optimal sample sizes with respect to the cost of the survey have been derived to validate the superiority of the proposed estimators, and the empirical investigation confirms the proposed estimators as highly preferable.
VL  - 10
IS  - 4
ER  -

Copy | Download