This article proposes various Searls-type ratio imputation methods (STRIM) on the lines of Ahmed et al. ( 2006 Ahmed, M. S. , O. Al-Titi, Z. Al-Rawi, and W. Abu-Dayyeh. 2006. Estimation of a population mean using different imputation methods. Stat. Trans. 7 (6):1247–1264. [Google Scholar] ). It is a well-known fact that the optimal ratio type estimator attains the MSE of regression estimator (or optimal difference estimator) but while using Searls-type transformation (STT) (Searls ( 1964 Searls, D. T. 1964. The utilization of a known coefficient of variation in the estimation procedure. J. Am. Stat. Assoc. 59:1225–1226. [Taylor & Francis Online], [Web of Science ®] [Google Scholar] )) this may not always happen. These STRIM are shown to perform better than the imputation procedures of Ahmed et al. ( 2006 Ahmed, M. S. , O. Al-Titi, Z. Al-Rawi, and W. Abu-Dayyeh. 2006. Estimation of a population mean using different imputation methods. Stat. Trans. 7 (6):1247–1264. [Google Scholar] ). The STRIM may even outperform the Searls type difference imputation methods (STDIM) proposed by us in our earlier work, Bhushan and Pandey ( 2016 Bhushan, S. , and A. P. Pandey. 2016. Optimal imputation of the missing data for estimation of population mean. Journal of Statistics and Management System 19 (6):755–69. [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ). This study is concluded with the numerical study along with the theoretical comparison.

This article examines the issue of population mean estimation utilizing past and present data in the form of an exponentially weighted moving average (EWMA) statistic under simple random sampling (SRS). We suggest memory-type logarithmic estimators and derive their properties, such as mean-square error (MSE) and bias up to a first-order approximation. Using the EWMA statistic, the conventional and novel memory-type estimators are compared. Real and artificial populations are used as examples to illustrate the theoretical findings. According to the empirical findings, memory-type logarithmic estimators are superior to the conventional mean estimator, ratio estimator, product estimator, logarithmic-type estimator, and memory-type ratio and product estimators.

In this article, we have addressed the issue of optimality under imputation by using Searls (1964) idea. We have proposed three new Searls-type difference (STD) methods for imputation of missing data. The resultant STD estimators are better than the estimators proposed by Kadilar and Cingi (2008) and Diana and Perri (2010). An analytical comparison shows that the proposed optimal methods are always better that the respective regression methods of imputation. Theoretical results are supported by an empirical study.

It is well known that ranked set sampling (RSS) is more efficient than simple random sampling (SRS). Furthermore, the presence of missing data vitiates the conventional results. Only a minuscule amount of work has been conducted under RSS with missing data. This paper makes a modest attempt to provide some efficient difference- and ratio-type imputation methods in the presence of missing values under RSS. The envisaged imputation methods are demonstrated to provide better results than the existing imputation methods. The theoretical results are enhanced by a computational analysis using real and hypothetically generated symmetric (Normal) and asymmetric (Gamma and Weibull) populations. The computational results show that the proposed imputation method outperforms the existing imputation methods in terms of its higher percent relative efficiency. Additionally, the impact of skewness and kurtosis on the efficiency of the suggested imputation methods has also been calculated.

In survey research, various types of estimators have been suggested that consider only the current sample information to compute the unknown population parameters. Therefore, we utilize the past sample information along with the current sample information in the form of hybrid exponentially weighted moving averages to suggest the memory type logarithmic estimators for time-based surveys. The expression of the mean square error of the suggested estimators is determined to the first order of approximation. A relative comparison of the suggested estimators with the existing estimators is performed and efficiency conditions are obtained. Further, a simulation study is accomplished using a hypothetically rendered population and a real data illustration to improve the theoretical results. The results of the simulation study and the real data application exhibit that the consideration of past and current sample information meliorates the efficiency of the suggested estimators.