Precision enhancement in variance estimation for complex environmental populations using adaptive cluster sampling.

Estimating dispersion in populations that are extremely rare, hidden, geographically clustered, and hard to access is a well-known challenge. Conventional sampling approaches tend to overestimate the variance, even though it should be genuinely reduced. In this environment, adaptive cluster sampling is considered to be the most efficient sampling technique as it provides generally a lower variance than the other conventional probability sampling designs for the assessment of rare and geographically gathered population parameters like mean, total, variance, etc. The use of auxiliary data is very common to obtain the precise estimates of the estimators by taking advantage of the correlation between the survey variable and the auxiliary data. In this article, we introduced a generalized estimator for estimating the variance of populations that are rare, hidden, geographically clustered and hard-to-reached. The proposed estimator leverages both actual and transformed auxiliary data through adaptive cluster sampling. The expressions of approximate bias and mean square error of the proposed estimator are derived up to the first-order approximation using Taylor expansion. Some special cases are also obtained using the known parameters associated with the auxiliary variable. The proposed class of estimators is compared with available estimators using simulation and real data applications.

Ln-type estimators for the estimation of the population mean of a sensitive study variable using auxiliary information.

In this article, we offered two ln-type estimators for the population mean estimation of a sensitive study variable by using the auxiliary information under the design of basic probability sampling. The Taylor and log series were used to derive the expressions of mean square error and bias up to the first order. Improved classes of proposed estimators are obtained by using conventional parameters associated with the supplementary variable to obtained precise estimates. Mathematical comparisons of the estimators have been made with the usual mean and ratio estimators using theoretical equations of mean square error. A simulation study is conducted for the evaluation of proposed estimator's implementation using four artificial populations generated through R-software with different choices of mean vectors and variance-covariance matrices. The demonstration of proposed ln-type estimators was implemented through the real data application.

Memory-type variance estimators using exponentially weighted moving average statistic in presence of measurement error for time-scaled surveys.

The present study suggested memory-type ratio and product estimators for variance estimation in the presence of measurement errors. We applied the exponentially weighted moving averages statistic which simultaneously utilizes the current and prior information for better estimation in surveys based on the time-scale. The expressions of approximate mean square errors of memory-type estimators are derived using Taylor series up to first order. Mathematical conditions are also obtained for which the suggested memory-type ratio and product estimators perform better than the conventional ratio and product estimators. The efficiency of the proposed estimators is observed using an extensive simulation study in the presence of measurement errors. A real data application is also carried out to support the mathematical expressions. From the results, it is shown that the use of prior sample information significantly increased the efficiency of the proposed estimators.

Optimized inferences of finite population mean using robust parameters in systematic sampling.

In this article, we have proposed a generalized estimator for mean estimation by combining the ratio and regression methods of estimation in the presence of auxiliary information using systematic sampling. We incorporated some robust parameters of the auxiliary variable to obtain precise estimates of the proposed estimator. The mathematical expressions for bias and mean square error of proposed the estimator are derived under large sample approximation. Many other generalized ratio and product-type estimators are obtained from the proposed estimator using different choices of scalar constants. Some special cases are also discussed in which the proposed generalized estimator reduces to the usual mean, classical ratio, product, and regression type estimators. Mathematical conditions are obtained for which the proposed estimator will perform more precisely than the challenging estimators mentioned in this article. The efficiency of the proposed estimator is evaluated using four populations. Results showed that the proposed estimator is efficient and useful for survey sampling in comparison to the other existing estimators.