In this paper, an extension of ratio and product type estimators be studied to estimate population mean in the context of post-stratification design while the data is affected by measurement errors. The expressions of extended estimators to calculate bias and MSE up to first order of approximation has been derived. By using some real data sets, an empirical study has been done to check the performance of estimators under measurement errors.
HansenM. H.HurwitzW. N. (1953). Sample survey methods and theory (Vol. I & II). John Wiley & Sons.
3.
HoltD.SmithT. M. F. (1979). Post-stratification. Journal of Royal Statistical Society A, 142, 33–46. https://doi.org/10.2307/2344652
4.
IgeA. F.TripathiT. P. (1989). Estimation of population mean using post-stratification and auxiliary information. Abacus, 18, 265–276.
5.
JagersP. (1986). Post stratification against bias in sampling. International Statistical Review, 55, 159–167. https://doi.org/10.2307/1403141
6.
JagersP.OdenA.TrulssonL. (1985). Post-stratification and ratio estimation: Usages of auxiliary information in survey sampling and opinion polls. International Statistical Review, 53, 221–238. https://doi.org/10.2307/1402887
ManishaR. K. (2001). An estimation of population mean in the presence of measurement errors. Journal of the Indian Society of Agricultural Statistics, 54(1), 13–18.
9.
MurthyM. N. (1967). Sampling theory and method. Statistical Publishing Society.
10.
ShalabhS. (1997). Ratio method of estimation in the presence of measurement errors. Journal of the Indian Society of Agricultural Statistics, 50(2), 150–155.
11.
ShuklaD.PathakS.ThakurN. S. (2012a). An estimator for mean estimation in presence of measurement error. Research & Reviews: A Journal of Statistics, 2(1), 1–8.
12.
ShuklaD.PathakS.ThakurN. S. (2012b). Class(es) of factor-type estimator in presence of measurement error. Journal of Modern Applied Statistical Methods, 11(2), 336–347. https://doi.org/10.22237/jmasm/1351742700
13.
SinghH. P.KarpeN. (2010). Effect of measurement errors on the separate and combined ratio and product estimators in stratified random sampling. Journal of Modern Applied Statistical Methods, 9(2). https://doi.org/10.22237/jmasm/1288584420
14.
StephanF. F. (1945). The expected value and variance of the reciprocal and other negative powers of a positive bernoullian variate. The Annals of Mathematical Statistics, 16, 50–61. https://doi.org/10.1214/aoms/1177731170
15.
YadavA.ThakurN. S.PareekS. (2024). Determining the effect of measurement errors and estimation of mean by factor-type estimator in simple random sampling. Journal of Modern Applied Statistical Methods, 23(1), 6. https://doi.org/10.56801/Jmasm.V23.i1.6