Research Article
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Year 2019, Volume 48, Issue 5, 1522 - 1546, 08.10.2019
https://doi.org/10.15672/hujms.465609

Abstract

References

  • [1] M. Ahmed, O. Al-Titi, Z. Al-Rawi and W. Abu-Dayyeh, Estimation of a population mean using different imputation methods , Statistics in Transition 7(6): 1247-1264, 2006.
  • [2] D. F. Heitjan and S. Basu, Distinguishing missing at random and missing completely at random, The Amer. Stat. 50 (3), 207-213, 1996.
  • [3] C. N. B. Herrera and A. I. Al-Omari, Ranked set estimation with imputation of the missing observations: the median estimator, Rev. Invest. Opera. 32 (1), 30-37, 2011.
  • [4] J. K. Kim, A. Navarro and W. A. Fuller, Replication variance estimation for two- phase stratified sampling, J. Amer. Statist. Assoc. 101 (473), 312-320, 2006.
  • [5] R. J. Little and D. B. Rubin, Statistical analysis with missing data, John Wiley and Sons, 2014.
  • [6] C. Mohamed , S. A. Sedory and S. Singh, Imputation using higher order moments of an auxiliary variable, Comm. Statist. Simulation Comput. 46 (8), 6588-6617, 2017.
  • [7] M. N. Murthy, Sampling theory and methods, Stat. Pub. Soc. 204/1, Barrackpore Tunk Road Calcutta, India, 1976.
  • [8] J. N. Rao and R. Sitter, Variance estimation under two-phase sampling with applica- tion to imputation for missing data, Biometrika 82 (2), 453-460, 1995.
  • [9] D. B. Rubin, Inference and missing data, Biometrika 63 (3), 581-592, 1976.
  • [10] J. Shabbir and S. Gupta, Estimation of the finite population mean in two phase sampling when auxiliary variables are attributes, Hacet. J. Math. Stat. 39 (1), 121-129, 2010.
  • [11] H. P. Singh and S. Kumar, Estimation of mean in presence of non-response using two phase sampling scheme, Statist. Papers 51 (3), 559-582, 2010.
  • [12] H. P. Singh, S. Kumar and M. Kozak, Improved estimation of finite population mean using sub-sampling to deal with non response in two-phase sampling scheme, Comm. Statist. Theory Methods 39 (5), 791-802, 2010.
  • [13] M. U. Sohail, J. Shabbir and S. Ahmed, Modified class of ratio and regression type estimators for imputing scrambling response, Pakistan J. Statist., 33 (4), 277-300, 2017.
  • [14] S. Singh, Advanced Sampling Theory With Applications: How Michael Selected Amy, Volume 2. Springer Science and Business Media, 2003.

Homogeneous imputation under two phase probability proportional to size sampling

Year 2019, Volume 48, Issue 5, 1522 - 1546, 08.10.2019
https://doi.org/10.15672/hujms.465609

Abstract

In this paper, we consider the problem of missing complete at random (MCAR) values in two phase probability proportional to size ($ pps $) sampling for the estimation of population mean.  A class of estimators is considered by the suitable use of auxiliary information with the traditional estimators for imputing the missing values. Theoretically, bias and mean squared errors of the proposed estimators are obtained up to the first order approximation. Two numerical studies are carried out for relative comparison of the proposed estimators with mean estimator under two phase $pps$ sampling for each situation.

References

  • [1] M. Ahmed, O. Al-Titi, Z. Al-Rawi and W. Abu-Dayyeh, Estimation of a population mean using different imputation methods , Statistics in Transition 7(6): 1247-1264, 2006.
  • [2] D. F. Heitjan and S. Basu, Distinguishing missing at random and missing completely at random, The Amer. Stat. 50 (3), 207-213, 1996.
  • [3] C. N. B. Herrera and A. I. Al-Omari, Ranked set estimation with imputation of the missing observations: the median estimator, Rev. Invest. Opera. 32 (1), 30-37, 2011.
  • [4] J. K. Kim, A. Navarro and W. A. Fuller, Replication variance estimation for two- phase stratified sampling, J. Amer. Statist. Assoc. 101 (473), 312-320, 2006.
  • [5] R. J. Little and D. B. Rubin, Statistical analysis with missing data, John Wiley and Sons, 2014.
  • [6] C. Mohamed , S. A. Sedory and S. Singh, Imputation using higher order moments of an auxiliary variable, Comm. Statist. Simulation Comput. 46 (8), 6588-6617, 2017.
  • [7] M. N. Murthy, Sampling theory and methods, Stat. Pub. Soc. 204/1, Barrackpore Tunk Road Calcutta, India, 1976.
  • [8] J. N. Rao and R. Sitter, Variance estimation under two-phase sampling with applica- tion to imputation for missing data, Biometrika 82 (2), 453-460, 1995.
  • [9] D. B. Rubin, Inference and missing data, Biometrika 63 (3), 581-592, 1976.
  • [10] J. Shabbir and S. Gupta, Estimation of the finite population mean in two phase sampling when auxiliary variables are attributes, Hacet. J. Math. Stat. 39 (1), 121-129, 2010.
  • [11] H. P. Singh and S. Kumar, Estimation of mean in presence of non-response using two phase sampling scheme, Statist. Papers 51 (3), 559-582, 2010.
  • [12] H. P. Singh, S. Kumar and M. Kozak, Improved estimation of finite population mean using sub-sampling to deal with non response in two-phase sampling scheme, Comm. Statist. Theory Methods 39 (5), 791-802, 2010.
  • [13] M. U. Sohail, J. Shabbir and S. Ahmed, Modified class of ratio and regression type estimators for imputing scrambling response, Pakistan J. Statist., 33 (4), 277-300, 2017.
  • [14] S. Singh, Advanced Sampling Theory With Applications: How Michael Selected Amy, Volume 2. Springer Science and Business Media, 2003.

Details

Primary Language English
Subjects Statistics and Probability
Journal Section Statistics
Authors

Muhammad Umair SOHAİL (Primary Author)
0000-0002-5440-126X


Javid SHABBİR
0000-0002-0035-7072


Cem KADİLAR This is me
0000-0003-4950-9660

Publication Date October 8, 2019
Published in Issue Year 2019, Volume 48, Issue 5

Cite

Bibtex @research article { hujms629930, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, pages = {1522 - 1546}, doi = {10.15672/hujms.465609}, title = {Homogeneous imputation under two phase probability proportional to size sampling}, key = {cite}, author = {Sohail, Muhammad Umair and Shabbir, Javid and Kadilar, Cem} }
APA Sohail, M. U. , Shabbir, J. & Kadilar, C. (2019). Homogeneous imputation under two phase probability proportional to size sampling . Hacettepe Journal of Mathematics and Statistics , 48 (5) , 1522-1546 . DOI: 10.15672/hujms.465609
MLA Sohail, M. U. , Shabbir, J. , Kadilar, C. "Homogeneous imputation under two phase probability proportional to size sampling" . Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1522-1546 <https://dergipark.org.tr/en/pub/hujms/article/629930>
Chicago Sohail, M. U. , Shabbir, J. , Kadilar, C. "Homogeneous imputation under two phase probability proportional to size sampling". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1522-1546
RIS TY - JOUR T1 - Homogeneous imputation under two phase probability proportional to size sampling AU - Muhammad Umair Sohail , Javid Shabbir , Cem Kadilar Y1 - 2019 PY - 2019 N1 - doi: 10.15672/hujms.465609 DO - 10.15672/hujms.465609 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1522 EP - 1546 VL - 48 IS - 5 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.465609 UR - https://doi.org/10.15672/hujms.465609 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Homogeneous imputation under two phase probability proportional to size sampling %A Muhammad Umair Sohail , Javid Shabbir , Cem Kadilar %T Homogeneous imputation under two phase probability proportional to size sampling %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 5 %R doi: 10.15672/hujms.465609 %U 10.15672/hujms.465609
ISNAD Sohail, Muhammad Umair , Shabbir, Javid , Kadilar, Cem . "Homogeneous imputation under two phase probability proportional to size sampling". Hacettepe Journal of Mathematics and Statistics 48 / 5 (October 2019): 1522-1546 . https://doi.org/10.15672/hujms.465609
AMA Sohail M. U. , Shabbir J. , Kadilar C. Homogeneous imputation under two phase probability proportional to size sampling. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1522-1546.
Vancouver Sohail M. U. , Shabbir J. , Kadilar C. Homogeneous imputation under two phase probability proportional to size sampling. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1522-1546.
IEEE M. U. Sohail , J. Shabbir and C. Kadilar , "Homogeneous imputation under two phase probability proportional to size sampling", Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 5, pp. 1522-1546, Oct. 2019, doi:10.15672/hujms.465609