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.
missing values, two phase sampling, imputation, probability proportional to size, auxiliary information
Primary Language  English 

Subjects  Statistics and Probability 
Journal Section  Statistics 
Authors 

Publication Date  October 8, 2019 
Published in Issue  Year 2019, Volume 48, Issue 5 
Bibtex  @research article { hujms629930, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651477X}, eissn = {2651477X}, 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) , 15221546 . 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 ): 15221546 <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 ): 15221546 
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  2651477X2651477X 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 2651477X2651477X %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): 15221546 . 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): 15221546. 
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): 15221546. 
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. 15221546, Oct. 2019, doi:10.15672/hujms.465609 