Generalized Chain Regression-cum-Chain Ratio Estimator for Population Mean under Stratified Extreme-cum-Median Ranked Set Sampling

Estimation of population mean of study variable Y suffers loss of precision in the presence of high variation in the data set. The use of auxiliary information incorporated in construction of an estimator under ranked set sampling scheme results in efficient estimation of population mean. In this paper, we propose an efficient generalized chain regression-cum-chain ratio type estimator to estimate finite population mean of study variable under stratified extreme-cum-median ranked set sampling utilizing information on two auxiliary variables. Mean square error (MSE) of the proposed generalized estimator is derived up to first order of approximation. The applications of the proposed estimator under symmetrical and asymmetrical probability distributions are discussed using simulation study and real-life data set for comparisons of efficiency. It is concluded that the proposed generalized estimator performs efficiently as compared to some existing estimators. It is also observed that the efficiency of the proposed estimator is directly proportional to the correlations between the study variable and its auxiliary variables.

A New Hybrid Exponentially Weighted Moving Average control chart using Mixture Ratio Estimator of Mean

In this paper, we propose a Hybrid Exponentially Weighted Moving Average (HEWMA) control chart based on a mixture ratio estimator of mean using a single auxiliary variable and a single auxiliary attribute (Moeen et al., [1]). We call it as Z- HEWMA control chart. The proposed control chart performance is evaluated using outof- control-Average Run Length (ARL1). The control limits of the proposed chart is based on estimator, its mean square errors. A simulated example is used to compare the proposed Z-HEWMA, traditional/simple EWMA chart and CUSUM control chart. From this study the fact is revealed that Z-HEWMA control chart shows more efficient results as compared to traditional/simple EWMA and CUSUM control charts. The Z-HEWMA chart can be used for efficient monitoring of the production process in manufacturing industries where auxiliary information about a numerical variable and an attribute is available.

Estimation of Domain Means from Business Surveys in the Presence of Stratum Jumpers and Nonresponse

Misclassified frame records (also called stratum jumpers) and low response rates are characteristic for business surveys. In the context of estimation of the domain parameters, jumpers may contribute to extreme variation in sample weights and skewed sampling distributions of the estimators, especially for domains with a small number of observations. There is limited literature about the extent to which these problems may affect the performance of the ratio estimators with nonresponse-adjusted weights. To address this gap, we designed a simulation study to explore the properties of the Horvitz-Thompson type ratio estimators, with and without smoothing of the weights, under different scenarios. The ratio estimator with propensity-adjusted weights showed satisfactory performance in all scenarios with a high response rate. For scenarios with a low response rate, the performance of this estimator improved with an increase in the proportion of jumpers in the domain. The smoothed estimators that we studied performed well in scenarios with non-informative weights, but can become markedly biased when the weights are informative, irrespective of response rate. We also studied the performance of the ’doubled half’ bootstrap method for variance estimation. We illustrated an application of the methods in a real business survey.

Ratio in Ratio Type Exponential Strategy for the Estimation of Population Mean

This paper is an attempt to develop an estimator for finite population mean. Motivated by Kiregyera (1984), a ratio in ratio type exponential strategy is developed for estimation of population mean in double sampling for stratification. To compare with relevant considered estimators, expressions for bias and mean squared error of the developed estimator have been derived. The developed estimator has been compared with usual unbiased estimator, Ige and Tripathi (1987), ratio estimator and ratio type exponential estimator given by Tailor et al (2014) theoretically as well as empirically.

Predicting Stand Volume by Number of Trees Automatically Detected in UAV Images: An Alternative Method for Forest Inventory

In this study, we estimate the forest stock volume by multiplying the number of trees detected remotely by the estimated mean individual volume of the population (individual approach). A comparison was made with the conventional inventory method (area approach), which included 100 simulations of a simple random sampling process and a Bootstrap resampling. The study area included three stands: stand 1, 16-year-old pine; stand 2, 7-year-old pine; and stand 3, 5-year-old eucalyptus. A census was carried out in each stand for the variables diameter and total height. Individual volume was estimated by a ratio estimator, and the sum of all volumes was considered as the total parametric volume. The area approach presented parametric values within the confidence interval for 91%, 94%, and 98% of the simulations for the three stands, respectively. The mean relative errors for the area approach were −3.5% for stand 1, 0.3% for stand 2, and −0.9% for stand 3. The errors in stands 1 and 3 were associated with the spatial distribution of the volume. The individual approach proved to be efficient for all stands, and their respective parametric values were within the confidence interval. The relative errors were 1% for stand 1, −0.7% for stand 2, and 1.8% for stand 3. For stand 1 and 3, this approach yielded better results than the mean values obtained by the area approach simulations (Bootstrap resampling). Future research should evaluate other remote sources of data and other forest conditions.

Robust Regression-Ratio-Type Estimators of the Mean Utilizing Two Auxiliary Variables: A Simulation Study

Many authors defined the modified version of the mean estimator by using two auxiliary variables. These proposed estimators highly depend on the calculated regression coefficients. In the presence of outliers, these estimators do not give satisfactory results. In this study, we improve the suggested estimators using several robust regression techniques while obtaining the regression coefficients. We compared the efficiencies between the suggested estimators and the estimators presented in the literature. We used two numerical examples and a simulation study to support these theoretical results. Empirical results show that the modified ratio estimator performs well in the presence of outliers when adopting robust regression techniques.

On the Strong Law of Large Numbers for Nonnegative Random Variables. With an Application in Survey Sampling

Strong laws of large numbers with arbitrary norming sequences for nonnegative not necessarily independent random variables are obtained. From these results we establish, among other things, stability results for weighted sums of nonnegative random variables. A survey sampling application is provided on strong consistency of the Horvitz--Thompson estimator and the ratio estimator.

A MODIFIED CALIBRATION APPROACH FOR RATIO ESTIMATOR IN STRATIFIED SAMPLING

Calibration is a technique for the adjustment of the original design weight to improve the precision of the survey. There is a dearth of information on calibration approach adapted for survey such that the survey cost is put into consideration. This research work developed a modified calibration approach for improving survey precision by considering the cost function. Data set on vegetable and tobacco productions (metric tonnes) were considered for this study. The data were obtained from the website of Food and Agriculture Organization. Data used was stratified based on geographical location. The population under study was divided into subpopulation of units, these subpopulations were non-overlapping homogenous sub- group. Observations were drawn within each stratum by simple random sampling with optimum allocation procedure. The proposed estimator was derived and used to determine the linear weight estimator of population parameters. The statistical properties of the derived estimator was examined. Using Lagrange multiplier, Mean Square Error and Relative Efficiency was obtained. The proposed estimator is found to be efficient