Improved predictive estimators for finite population mean using Searls technique

Estimation of Finite Population Mean Using Ratio Estimator Based on Known Median of Auxiliary Variable in the Presence of Non-Response

“…It was noted that the Hansel and Hurwitz estimator is unbiased. However, the estimator suffers from a high mean squared error [10]. Therefore, the present study found a need to incorporate median of the auxiliary information in the development of a more efficient estimator in terms of the Mean squared error.…”

Novel predictive estimators using ranked set sampling

“…Later on, Reference 2 demonstrated that when product estimator $$$ {T}_4,\mathrm{srs} $$$ is utilized as a predictor, the predictive estimator $$$ {t}_4,\mathrm{srs} $$$ is rather different from the usual product estimator $$$ {T}_4,\mathrm{srs} $$$. Recently, Reference 5 demonstrated that when Reference 3 exponential ratio and product estimators are used as a predictor, the corresponding predictive estimators are rather different from the natural estimators $$$ {T}_i,\mathrm{srs},\kern0.3em i=5,6 $$$, respectively.…”

“…Reference 29 developed a method for improving the efficacy of the traditional estimators by multiplying a scalar $$$ \theta \kern0.3em \left(\mathrm{say}\right) $$$ whose optimum value is based on the coefficient of variation that is a quite stable quantity. Following References 5,29 defined the undermentioned improved estimators corresponding to the predictive estimators $$$ {t}_i,\mathrm{srs},\kern0.3em i=1,2,3,4 $$$ as $$$$ {t}_7,\mathrm{srs}\kern0.5em ={\theta}_1{t}_1,\mathrm{srs}={\theta}_1{\overline{y}}_s, $$$$ $$$$ {t}_8,\mathrm{srs}\kern0.5em ={\theta}_2{t}_2,\mathrm{srs}={\theta}_2{\overline{y}}_s\left(\frac{{\overline{X}}_{\overline{s}}}{{\overline{x}}_s}\right), $$$$ …”

“…Recently, following References 5,29 developed the undermentioned modified estimators corresponding to the predictive estimators $$$ {t}_i,\mathrm{srs},i=5,6 $$$ as $$$$ {t}_{11},\mathrm{srs}\kern0.5em ={\theta}_5{t}_5,\mathrm{srs}={\theta}_5\left[f{\overline{y}}_s+\left(1-f\right){\overline{y}}_s\exp \left\{\frac{N\left(\overline{X}-{\overline{x}}_s\right)}{N\left(\overline{X}+{\overline{x}}_s\right)-2n{\overline{x}}_s}\right\}\right], $$$$ …”

“…Subsequently, the exponential ratio and product estimators suggested by Reference 3 were used as predictors to develop predictive estimators for the population mean by Reference 4. The readers may also see some newly existing researches, namely, References 5‐8 for extensive knowledge of predictive estimation approach.…”