Estimation with incomplete frames using varying probability sampling with replacement

Article type: Research Article

Authors: Jyoti, ^{a; *} | Pareek, Sarla^a | Gupta, P.C.^b

Affiliations: [a] Banasthali Vidyapith, Rajasthan, India | [b] Veer Narmad South Gujarat University, U.M. Road, Surat, Gujarat, India

Correspondence: [*] Corresponding author: Jyoti, Banasthali Vidyapith, Rajasthan 304022, India. Tel.: +91 8171665089; E-mail: jyotidev626@gmail.com.

Abstract: Sampling frames are mostly incomplete in large scale surveys. This paper suggests the use of probability proportional to size with replacement (PPSWR) sampling scheme for estimation of population mean with an incomplete frame. The variance of the estimators has been obtained and its efficiency has been compared with Agarwal and Gupta (2008) estimator when the frame is not complete. The results obtained have been illustrated with the help of hypothetical data. The problem of determining optimum sample size and retainment factor has also been discussed using a suitable linear cost function.

Keywords: Incomplete sampling frames, variance, efficiency, Hansen Hurwitz estimator, probability proportional to size (PPS) sampling, cost function, Lagrange’s constant multiplier

DOI: 10.3233/MAS-221379

Journal: Model Assisted Statistics and Applications, vol. 18, no. 1, pp. 85-91, 2023