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To obtain reliable estimates of population parameters, data that is sampled for estimation must accurately represent the underlying population. Sampled data that is representative of the underlying population depends also on the sampling technique that was used in obtaining them. This is very important since sampling bias could lead to over or under estimation of parameters. Ranked Set Sampling is considered to be a better alternative to the classical sampling designs in obtaining such data. Ranked Set Sampling is designed to minimize the number of measured observations required to achieve a desired precision in making inferences, and thus it is more economical to use for the purposes of estimation, compared to the classical sampling designs. This is also an added advantage in cases where it is difficult to obtain data. Many estimators have been developed recently for the estimation of finite population mean under ranked set sampling. This paper aims to improve estimation by modifying an existing estimator using a simple linear combination of the known population mean, square root of the known coefficient of variation, and the known median of an auxiliary variable. The theoretical properties of the proposed estimator, such as the bias and mean squared error were derived up to the first order of approximation, using Taylor's expansion. The bias, mean squared error, absolute relative bias, and the relative efficiency were used as means of evaluation and comparison between the proposed modified estimator and its competitors. The R software was used to aid computations. Empirical applications to real data showed that the proposed modified estimator is superior to the competing estimators that were compared since it has least bias, the least mean squared error, the least absolute relative bias, and the highest relative efficiency in all sample sizes that were considered. The bias and mean squared error of the modified estimator under Ranked Set Sampling was found to be smaller than those of the existing estimators that were compared. Hence it is more efficient and capable of providing reliable estimates than the existing estimators that were compared and so we recommend that it should be used in survey estimations. [ABSTRACT FROM AUTHOR]

Cluster randomized experiments and estimator comparisons are well-documented topics. In this paper, using the datasets of the popular vote in the presidential elections of the United States of America (2012, 2016, 2020), we evaluate the properties (SE, MSE) of three cluster sampling estimators: Ratio estimator, Horvitz–Thompson estimator and the linear regression estimator. While both the Ratio and Horvitz–Thompson estimators are widely used in cluster analysis, we propose a linear regression estimator defined for unequal cluster sizes, which, in many scenarios, performs better than the other two. The main objective of this paper is twofold. Firstly, to indicate which estimator is most suited for predicting the outcome of the popular vote in the United States of America. We do so by applying the single-stage cluster sampling technique to our data. In the first partition, we use the 50 states plus the District of Columbia as primary sampling units, whereas in the second one, we use 3112 counties instead. Secondly, based on the results of the aforementioned procedure, we estimate the number of clusters in a sample for a set standard error while also considering the diminishing returns from increasing the number of clusters in the sample. The linear regression estimator is best in the majority of the examined cases. This type of comparison can also be used for the estimation of any other country's elections if prior voting results are available. [ABSTRACT FROM AUTHOR]

Cluster randomized experiments and estimator comparisons are well-documented topics. In this paper, using the datasets of the popular vote in the presidential elections of the United States of America (2012, 2016, 2020), we evaluate the properties (SE, MSE) of three cluster sampling estimators: Ratio estimator, Horvitz–Thompson estimator and the linear regression estimator. While both the Ratio and Horvitz–Thompson estimators are widely used in cluster analysis, we propose a linear regression estimator defined for unequal cluster sizes, which, in many scenarios, performs better than the other two. The main objective of this paper is twofold. Firstly, to indicate which estimator is most suited for predicting the outcome of the popular vote in the United States of America. We do so by applying the single-stage cluster sampling technique to our data. In the first partition, we use the 50 states plus the District of Columbia as primary sampling units, whereas in the second one, we use 3112 counties instead. Secondly, based on the results of the aforementioned procedure, we estimate the number of clusters in a sample for a set standard error while also considering the diminishing returns from increasing the number of clusters in the sample. The linear regression estimator is best in the majority of the examined cases. This type of comparison can also be used for the estimation of any other country’s elections if prior voting results are available.

This paper offers an improved memory-type ratio estimator in stratified random sampling under linear and non-linear cost functions. The issue is given as all integer non-linear programming problems (AINLPPs). The sampling properties mainly the bias and the mean squared error of the introduced estimator are derived up to the first order of approximation. The optimum value of the characterizing scalar is obtained by the Lagrange method of maxima–minima. The least value of the MSE of the suggested estimator is also obtained for this optimum value of the charactering constant. The suggested estimator is compared both theoretically and empirically with the competing estimators. Under this setup, the optimum allocation with mean square error of the suggested estimator is attained, and the estimator is compared to other comparable estimators. The AINLPP is solved using the genetic programming approach, which is applied to both actual and simulated data sets from a bivariate normal distribution. [ABSTRACT FROM AUTHOR]

The transformation technique can assist in improving the efficiency of the estimators in terms of bias and mean square error reduction. A class of ratio estimators for estimating population mean utilizing the transformation of an auxiliary variable has been proposed under stratified random sampling. The bias and mean square error of the proposed estimators up to the first order of approximation are obtained. Simulation studies and an application to rubber data in Thailand are investigated to compare the performance of the proposed class of estimators with existing estimators, the results show that the proposed class of estimators performs much better than other existing estimators under given conditions. [ABSTRACT FROM AUTHOR]

An improved ratio-type calibrated estimator was developed using the logarithmic mean in the calibration constraint for the stratified random sampling scheme. The proposed estimator was extended in the case of stratified double sampling and compared with the estimators given by Tracy et al. (2003) together its ratio-type estimators, as well as Nidhi et al. (2017) and Khare et al. (2022). A simulation study was also carried out on both a real and artificial dataset in order to evaluate the performance of the proposed estimator compared to the existing estimators. [ABSTRACT FROM AUTHOR]

In the majority of sample surveys, the variable of interest might have sensitive characteristics. Since we frequently get unrealistic responses from respondents during interviews as employing the direct method is not seen logical in these situations. To tackle this difficulty, the randomized response technique is good substitute for the direct method. The respondent is reassured that there would not be any issues will your response when using the randomized response technique as it protects privacy and secrets. In this paper, we propose a novel quantitative three-stage randomized response technique. Using simulation with R software, we prove that the results obtained from the proposed method are ideal. We suggest ratio and product type estimators by using the auxiliary information to enhance the efficiency of estimators. It is demonstrated that these estimators are superior for the conventional ones in special situations and in applied task, the use of auxiliary variable improves the estimation of the average cheating of Shahid Chamran university of Ahvaz students. The main objective is to increase the average sensitive reaction by utilizing the auxiliary variable.

In this investigation, we examined the impact of employing simple random sampling on the stratification points pertaining to the two independent variables. The study focused on a variable (X) exhibiting a robust correlation, and we employed a combination of ratio and product estimators to select a representative sample and establish the population mean. By maintaining a comprehensive superpopulation framework, we successfully identified concise equations that effectively reduced the overall variability within the dataset. To reveal the underlying nature of these mathematical derivations, we employed the cumulative cube roots rule to determine nearly optimal stratification points for the two research variables. The validity of this suggested rule was assessed through rigorous testing utilizing empirical and simulated data obtained from diverse distributions.

In this paper, an unbiased ratio estimator based on Tin (1965), an unbiased product estimator based on Robson (1957) and an unbiased estimator based on Mahanty and Mishra (2020) by using auxiliary information was developed under two-phase sampling. The efficiency of the estimators is shown both theoretically and numerical illustration. The unbiased estimator based on Mahanty and Mishra is more efficient than other estimators. [ABSTRACT FROM AUTHOR]

This paper suggests a calibration ratio type estimator of the population mean in case of the stratified random sampling using a logarithmic mean as a calibration constraint. The result so obtained has been extended in case of stratified double sampling. The simulation study has also supported the performance of the suggested estimators over the existing estimators given by Singh et al. (1998) and Clement (2015) on the basis of two artificial data sets. [ABSTRACT FROM AUTHOR]

In this paper, we consider the situation where the underlying distribution of the study variable is not normally distributed. Under such situations, we propose ratio and product based estimators for the finite population mean in simple random sampling using known auxiliary information based on order statistics. We obtain the expressions for biases and mean square errors (MSEs) of the proposed estimators, which show that the proposed estimators have less MSEs and biases than other existing estimators. Simulations have been studied under various super-population models. A real life application is also provided. Robustness properties of the proposed estimators have been studied via simulations. Confidence intervals (CIs) show that the proposed estimators have shorter CIs of estimates than those of the existing estimators. [ABSTRACT FROM AUTHOR]

Estimation of population mean is a determined subject issue in sampling surveys and many efforts have been paid by various researchers to enhance the precision of the estimates by utilizing the correlated auxiliary information. In connection with this, we suggest an improved exponential ratio-cum-ratio estimator using transformed auxiliary variables under ranked set sampling scheme. Theoretical comparison between estimators is made in terms of mean square errors (MSEs), percentage relative efficiencies (PREs), and percentage relative root mean squared error (PRRMSE). The numerical expression for the bias and MSE of the suggested estimator is derived up to first order of approximation. Based on the results of actual data sets and a simulation study, it is found that the suggested estimator perform well as compared to its existing counterparts.

The issue of fine particulate matter in Thailand, especially in Northern Thailand, is an urgent problem that needs to be solved because of potential harm to human health. Prior estimates of fine particulate matter help planning how to reduce it. The daily fine particulate matter data reports usually contain some missing values. An improved ratio estimator has been suggested for population total under unequal probability sampling without replacement. The improved estimator is studied under a reverse framework when the nonresponse mechanism is not uniform, called missing at random nonresponse, which is more convenient to apply in practice. The variance and its associated estimator are investigated in theory. Simulation studies are used to assess the suggested estimator’s performance. The new estimator is also applied to estimate fine particulate matter in Northern Thailand. The results show that the suggested estimator under the missing at random nonresponse mechanism performs well, as opposed to the existing estimator under missing completely at random assumption. The estimated fine particulate matter levels in Northern Thailand from the proposed estimator give a lesser variance than the existing one.

In this manuscript, a generalized class of estimators has been developed for estimating finite population means in a Ranked Set Sampling (RSS) scheme. The expressions for bias and Mean Square Error (MSE) of the proposed class of estimators have been derived up to the first order of approximation. Some estimators are shown to be a member of the proposed class. The proposed class of estimators has been compared through the MSE criterion over the other existing member estimators of the proposed class of estimators. The theoretical conditions are obtained under which the proposed class of estimators has performed better. Efficiency comparisons, empirical studies, and simulation studies also delineate the soundness of our proposed generalized class of estimators under RSS. [ABSTRACT FROM AUTHOR]

Lack of data due to missing observations may lead to serious issues in statistical analysis. Filling in missing values with possible estimated values using the imputation method could help to eliminate this problem. A new imputation technique has been suggested along with a population mean estimator when missing observations occur in the study. The bias and mean square error of the new estimator are investigated in theory. The performance of the new estimator is examined using applications to air pollution data. The results show that the new imputation method can be used to estimate the population mean leading to minimum mean square error relative to some existing estimators. [ABSTRACT FROM AUTHOR]

The issue of fine particulate matter in Thailand, especially in Northern Thailand, is an urgent problem that needs to be solved because of potential harm to human health. Prior estimates of fine particulate matter help planning how to reduce it. The daily fine particulate matter data reports usually contain some missing values. An improved ratio estimator has been suggested for population total under unequal probability sampling without replacement. The improved estimator is studied under a reverse framework when the nonresponse mechanism is not uniform, called missing at random nonresponse, which is more convenient to apply in practice. The variance and its associated estimator are investigated in theory. Simulation studies are used to assess the suggested estimator's performance. The new estimator is also applied to estimate fine particulate matter in Northern Thailand. The results show that the suggested estimator under the missing at random nonresponse mechanism performs well, as opposed to the existing estimator under missing completely at random assumption. The estimated fine particulate matter levels in Northern Thailand from the proposed estimator give a lesser variance than the existing one. [ABSTRACT FROM AUTHOR]

The use of multi-auxiliary variables helps in increasing the precision of the estimators, especially when the population is rare and hidden clustered. In this article, four ratio-cum-product type estimators have been proposed using two auxiliary variables under adaptive cluster sampling (ACS) design. The expressions of the mean square error (MSE) of the proposed ratio-cum-product type estimators have been derived up to the first order of approximation and presented along with their efficiency conditions with respect to the estimators presented in this article. The efficiency of the proposed estimators over similar existing estimators have been assessed on four different populations two of which are of the daily spread of COVID-19 cases. The proposed estimators performed better than the estimators presented in this article on all four populations indicating their wide applicability and precision. [ABSTRACT FROM AUTHOR]

The exponential weighted moving average (EWMA) statistic is utilized the past information along with the present to enhance the efficiency of the estimators used for estimating the population parameters. In this study, the EWMA statistic is used for the estimation of population mean with suitable auxiliary information. The memory type ratio and product estimators are proposed under ranked-based sampling (RBS) schemes including extreme ranked set sampling, median ranked set sampling, and quartile ranked set sampling. The expressions of mean square errors (MSE) of the proposed estimators are derived. An extensive simulation study is conducted to evaluate the performance of the proposed estimators. An empirical study is presented based on real-life data that supports the findings of the simulation study. [ABSTRACT FROM AUTHOR]

To propose a new memory type estimator of Population Mean in two phase simple random sampling with one auxiliary using EWMA for time scaled surveys and to compare the proposed estimator with related previous estimator. Using Two-Phase Sampling technique, a generalized difference-cum-ratio type estimator has been proposed for estimating the population mean. The expressions for bias and mean square error of proposed estimator have been obtained. The conditions under which proposed estimator is better than the regression estimator and mean per unit estimator have also been obtained. Simulation study has also been done to support the results by generating data. Exponentially weighted moving average (EWMA) statistic is a memory type statistic that used present and past information to estimate the population parameter. This study utilizes EWMA statistic to propose a ratio and product estimator for the surveys based on time scale. The usual ratio and product estimators consist of only current sample information, whereas the proposed estimators contains of current as well as past sample information. The mean square error expressions of the proposed estimators are derived and mathematical conditions are established to prove the efficiency of proposed estimators. It is revealed from the results of simulation study that utilization of the past samples information excels the performance of estimator in terms of efficiency. [ABSTRACT FROM AUTHOR]

We describe five asymptotically unbiased estimators of intervention effects on event rates in nonmatched and matched-pair cluster randomized trials, and we present a bias-corrected version of the estimators for use when the number of clusters is small. The estimators are the ratio of mean counts (r 1), ratio of mean cluster-level event rates (r 2), ratio of event rates (r 3), double ratio of counts (r 4), and double ratio of event rates (r 5). r 1, r 2, and r 3 estimate the total effect, which comprises the direct and indirect effects; r 4 and r 5 estimate the direct effect. We describe a new command, crtrest, that provides these ratio estimators and their standard errors in nonmatched and matched-pair cluster randomized trials. [ABSTRACT FROM AUTHOR]

Ranked set sampling is an approach to data collection originally combines simple random sampling with the field investigator's professional knowledge and judgment to pick places to collect samples. Alternatively, field screening measurements can replace professional judgment when appropriate and analysis that continues to stimulate substantial methodological research. The use of ranked set sampling increases the chance that the collected samples will yield representative measurements. This results in better estimates of the mean as well as improved performance of many statistical procedures. Moreover, ranked set sampling can be more cost-efficient than simple random sampling because fewer samples need to be collected and measured. The use of professional judgment in the process of selecting sampling locations is a powerful incentive to use ranked set sampling. This paper is devoted to the study, we introduce an approach to the mean estimators in ranked set sampling. The amount of information carried by the auxiliary variable is measured with the on populations and samples and to use this information in the estimator, the basic ratio and the generalized exponential ratio estimators are as an improved form of a difference cum exponential ratio type estimator under the ranked set sampling in order to estimate the population mean ... of study variate Y using single auxiliary variable X. The expressions for the mean squared error of propose estimator under ranked set sampling is derived and theoretical comparisons are made with competing estimators. We show that the proposed estimator has a lower mean square error than the existing estimators. In addition, these theoretical results are supported with the aid of some real data sets using R studio. Therefore, Under RSS architecture, a better difference cum exponential ratio type estimator has been suggested. The estimator's mathematical form has been developed, and its efficiency requirements have been developed in relation to various already-existing estimators from the literature. By imputing various values for the constants used in the creation of our proposed estimator, we also provide several specific situations of our estimator. [ABSTRACT FROM AUTHOR]

In current manuscript, two modified ratio estimators are suggested for estimating population mean utilizing auxiliary information. For the proposed estimators, mathematical expressions like Bias and Mean Square Error (MSE) are studied for approximation up to one order. The least MSE value for the suggested class is also obtained for the optimum value of the kappa constant (K). Moreover, theoretical comparison along with empirical study based on real data sets is carried out for suggested estimators and competing estimators and it is concluded that the proposed class of estimators are better and more efficient than other mentioned existing estimators for population mean. [ABSTRACT FROM AUTHOR]

In this article, we study the situation of observations whose ranks cannot be determined for the auxiliary variable in the Ranked Set Sampling (RSS) method. Therefore, we examine the case of tie information for ratio estimators of the population mean. We propose a new exponential ratio estimator using the modified isotonic estimator for this situation. Simulation results show that the proposed estimator is more efficient than the other estimators in literature. In addition, when we examine the recent COVID-19 pandemic situation, we see that the data is suitable for this structure. We can also see from the real data that the proposed estimator gives better results. [ABSTRACT FROM AUTHOR]

The ratio, product, difference estimators, and unbiased estimator under systematic sampling scheme has been studied in the presence of measurement error. The methods of estimation have been proposed for the estimation of the finite population mean. To exhibit the effect of measurement error, the study variable and auxiliary variable are supposed to be observed with measurement error. The properties of estimators' viz. bias and MSE have been obtained. The simulation study has been conducted to compute the effect of measurement error on the MSE for the different levels of correlation coefficient and different levels of error variance. [ABSTRACT FROM AUTHOR]

In this article, a class of Poisson-regression based estimators has been proposed for estimating the finite population mean in simple random sampling without replacement (SRSWOR). The Poisson-regression model is the most common method used to model count responses in many studies. The expression for bias and mean square error (MSE) of proposed class of estimators are obtained up to first order of approximation. The proposed estimators have been compared theoretically with the existing estimators, and the condition under which the proposed class of estimators perform better than existing estimators have been obtained. Two real data sets are considered to assess the performance of the proposed estimators. Numerical findings confirms that the proposed estimators dominate over the existing estimators such as Koc (2021) and Usman et al. (2021) in terms of mean squared error. [ABSTRACT FROM AUTHOR]

A general scrambled randomized response model that aims to regulate a realistic swapping between efficiency and privacy protection is developed. The basic initiative is to offer a hotchpotch of many different scrambling randomized response models, including many existing additive, subtractive, multiplicative and general scrambling randomized response models. A more efficient and generalized class of estimators for estimating the population mean based on two non-sensitive auxiliary variables is employed using the general scrambling randomized response model. The bias and mean square error of all estimators are computed from a simulation, along with empirical studies by assuming the additive model, multiplicative model and proposed generalized scrambled model in separate tables. The simulation and empirical results demonstrate that the proposed estimators are more efficient than the existing ones. It is also shown that the gain in efficiency is higher when the proposed model is used. [ABSTRACT FROM AUTHOR]

In survey sampling, to handle the situation where human bias arises due to some personal or illegal questions, the randomized response technique developed by Warner is used [1]. The calibration technique is used to reduce the bias between the original and estimated weights in stratified random sampling. We estimate the population total, using the calibration estimation technique in which the study variable corresponds to a scrambled variable due to the randomized response technique. We have discussed the estimation procedure of population total and suggested some new estimators, such as ratio and exponential estimators, using different distance measures and calibration constraints. The simulation study has been applied tn newly developed estimators in sensitive survey sampling using a scrambled randomized response (SRR). We see that exponential estimators perform better than ratio and simple estimators of the total stratified random samplings when the variable of interest is sensitive. [ABSTRACT FROM AUTHOR]

This document summarizes results and details of the study on the estimation of canine and feline populations, with some of their characteristics, in each of the Quindío municipalities under departmental jurisdiction. The collection of information on the populations, plus the analysis of characteristics of coexistence with the human population, responds to a need of the Secretary of Health of the Department of Quindío to include this topic in its Development Plan 2020-2023, responding to the objective of "Promoting the reduction of exposure to environmental, sanitary and biological conditions and risk factors, to mitigate the contingencies and damages produced by transmissible diseases (zoonosis and vectors)". [ABSTRACT FROM AUTHOR]

In the current investigation, we have suggested a Difference Cum-Exponential Type Efficient Estimator of Population variance of the study variable using information on the auxiliary variable. Up to the first order of approximation, the proposed estimator's bias and mean square error (MSE) expressions are derived and suggested optimum estimator is also found, with its optimal qualities are investigated. The suggested estimator is proven to be more competent than sample variance, classic ratio estimators based on Isaki, Singh et al. and Kadilar and Cingi estimators in [1-3]. Numerical study is also carried out by using real data sets. [ABSTRACT FROM AUTHOR]

This paper proposes and investigates the bivariate, the marginal distribution functions and quantiles estimators and their asymptotic properties for naïve, ratio, and difference estimators based on the bivariate stratified simple random sampling (BVSSRS) and bivariate stratified ranked set sampling designs (BVSRSS). We demonstrate that the proposed estimators using BVSRSS and BVSSRS are consistent and asymptotically normally distributed. Improved performance of the proposed estimators using BVSRSS compared to BVSSRS supported through an intensive simulation study. The derivation of the optimal allocation based on BVSSRS and BVSRSS is provided. The National Health and Nutrition Examination Survey (NHANES) data is used to illustrate the methods. [ABSTRACT FROM AUTHOR]

The evaluation of wild boar density in a hunting district can be performed by accurate drive counts of boars within the drive areas assigned to each hunting team. Because a complete driving of all the areas is prohibitive, only a subset is driven in a hunting occasion. Results are highly dependent on the subjective choice of these areas. In this study, an objective design-based approach is considered in which areas to be driven are randomly selected one per team in accordance with the one-per-stratum sampling scheme. Because the areas assigned to hunting teams are likely to be close to each other, the one-per-stratum sampling is likely to achieve samples of evenly spread areas. Then, the subsequent step is to choose the selection criterion for the areas and the estimation criterion for exploiting or not the information provided by area sizes. To this purpose, three sampling strategies are considered, together with methods to estimate their precision. These strategies are checked and compared by means of a simulation study performed on artificial populations constructed from the list of drive areas settled in the Province of Massa–Carrara (Italy) and partitioned among 39 hunting teams. Results from artificial populations give clear insights about the most suitable strategy to be used. Drive counts performed in this province in two hunting occasions during 2019 within 39 areas selected by one-per-stratum sampling are adopted as case studies. [ABSTRACT FROM AUTHOR]

Cost-effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time-consuming. In this article, we investigate ratio-type estimators of the population mean of the study variable, involving either the first or the third quartile of the auxiliary variable, using ranked set sampling (RSS) and extreme ranked set sampling (ERSS) schemes. The properties of the estimators are obtained. The estimators in RSS and ERSS are compared to their counterparts in simple random sampling (SRS) for normal data. The numerical results show that the estimators in RSS and ERSS are significantly more efficient than their counterparts in SRS. [ABSTRACT FROM AUTHOR]

Recently, a few studies have presented the problem of estimation of the mean for a finite homogenous population considering the joint influence of non-response and measurement errors and following the assumption that population mean of auxiliary variable is available. However, in real situations the population under observation may not be homogeneous and population mean of the auxiliary variable may also not be available. Therefore, in this study, we present new estimators which are the generalized form of the difference-cum-exponential type estimator of the finite population mean in the presence of non-response and measurement errors in two-phase simple random sampling and stratified random sampling. The expressions for mean square error and bias of the proposed estimators are shown under the first order approximation in each sampling design. Theoretically, it has been shown that the proposed estimators are more efficient than some existing estimators in both sampling designs. A numerical study has also been carried out using two different simulated populations under simple random sampling designs as well as under stratified random sampling design to support the theoretical results. Numerical results show that the proposed estimators perform more efficiently than some modified versions of the existing estimators in both sampling designs. [ABSTRACT FROM AUTHOR]

We consider five asymptotically unbiased estimators of intervention effects on event rates in non‐matched and matched‐pair cluster randomized trials, including ratio of mean counts r1, ratio of mean cluster‐level event rates r2, ratio of event rates r3, double ratio of counts r4, and double ratio of event rates r5. In the absence of an indirect effect, they all estimate the direct effect of the intervention. Otherwise, r1, r2, and r3 estimate the total effect, which comprises the direct and indirect effects, whereas r4 and r5 estimate the direct effect only. We derive the conditions under which each estimator is more precise or powerful than its alternatives. To control bias in studies with a small number of clusters, we propose a set of approximately unbiased estimators. We evaluate their properties by simulation and apply the methods to a trial of seasonal malaria chemoprevention. The approximately unbiased estimators are practically unbiased and their confidence intervals usually have coverage probability close to the nominal level; the asymptotically unbiased estimators perform well when the number of clusters is approximately 32 or more per trial arm. Despite its simplicity, r1 performs comparably with r2 and r3 in trials with a large but realistic number of clusters. When the variability of baseline event rate is large and there is no indirect effect, r4 and r5 tend to offer higher power than r1, r2, and r3. We discuss the implications of these findings to the planning and analysis of cluster randomized trials. [ABSTRACT FROM AUTHOR]

In sample surveys, auxiliary information is used for estimation to improve the efficiency of estimators. Increased precision can be obtained when the variable under study is highly correlated with auxiliary information. In this study, the sample size has been used as information for improved estimation of population mean of the main variable under study. A new modified generalized ratio type estimator of population mean has been proposed and the efficiency was examined using Murthy (1967) and Mukhopadhyay (2009) dataset. The large sample properties, the bias and the mean squared error of the newly proposed modified ratio estimator were obtained up to first order of approximation. The optimum value of the characterizing scalar which minimizes the mean squared error was obtained and the minimum value of the mean squared error of the proposed modified ratio estimator for this optimum value was also obtained. A theoretical comparison of the proposed modified ratio estimators was made with the other existing related estimators of population mean using auxiliary information. The conditions under which the proposed modified ratio estimators perform better than the other existing estimators of population mean are given. A numerical study was also carried out to see the performances of the proposed modified ratio estimators and some existing related ratio estimators of population mean and verify the conditions under which the proposed modified ratio estimators are better than some other existing related ratio estimators considered. It was shown that the proposed modified ratio estimators perform better than some existing related ratio estimators as they are having lower mean squared errors. [ABSTRACT FROM AUTHOR]

The article proposes a ratio estimator of population mean using information on population median of the study variable, which is known under stratified random sampling. The mean square error of the proposed estimator with linear cost function is obtained and a comparative study of the estimator with existing related estimators is carried out. The solution of the problem is achieved with the help of integer programing using Lagrange multiplier technique using both the real data set and the data simulated from a bivariate normal distribution. Both the data sets demonstrate that the proposed estimator is more efficient than the other existing estimators. [ABSTRACT FROM AUTHOR]

Erroneous enumerations in the census include multiple enumerations and other errors. The linear estimator for estimating these errors currently used in several countries leads to underestimation when the sample used for the estimation comprises few of these errors. The "ratio estimator" of the total number of erroneous enumerations overcomes this difficulty. This is the one used by China for the 2020 census. Empirical analysis shows that the ratio estimator provides a smaller sampling error than the linear estimator. [ABSTRACT FROM AUTHOR]

Rank Set Sampling (RSS) is an alternative to simple random sampling was proposed by McIntyre (1952): Under such sampling scheme various authors have proposed the ratio rank set estimators in order to estimate the population parameters by using OLS (Ordinary Least Square) method. A big issue emerge that when outliers are present in data in that case all the estimators suggested by different authors can give distorted results as OLS is very sensitive to outliers. So in the present study we mainly focus on this issue and adapted the Huber M estimation Technique on the estimator suggested by Al-Odat (2009) instead of OLS, in order to get precise results in case of presence of outliers in data. [ABSTRACT FROM AUTHOR]

We propose exponential ratio type estimator to estimate the population mean under non-response scheme in this article. The expressions for the Bias and Mean Square Error (MSE) are derived and theoretical comparisons are made to examine the efficiencies of the estimator with the estimators considered by many researchers in the literature. In the end of the article, the efficiencies of the proposed estimator is supported numerically by three different data sets. According to theoretical and numerical results, it is concluded that the proposed estimator is the most efficient estimator among all others and can be applied successfully. [ABSTRACT FROM AUTHOR]

Exponentially weighted moving average (EWMA) statistic is a memory type statistic that used present and past information to estimate the population parameter. This study utilizes EWMA statistic to propose a ratio and product estimator for the surveys based on time scale. The usual ratio and product estimators consist of only current sample information, whereas the proposed estimators consist of current as well as past sample information. The mean square error expressions of the proposed estimators are derived and mathematical conditions are established to prove the efficiency of proposed estimators. It is revealed from the results of simulation study that utilization of the past samples information excels the performance of estimator in terms of efficiency. Two real life examples are presented to demonstrate the use of proposed estimators. [ABSTRACT FROM AUTHOR]

This paper proposes two new classes of ratio estimators for population mean when information on a known auxiliary variable is available in simple random sampling. A combined family of ratio estimators for estimating population mean by combining the two new estimators together in order to minimize the mean square error (MSE) is then suggested. The expressions for the bias and mean square error of all proposed estimators up to the first order of approximation were obtained. The performance of the proposed estimators was compared with that of existing estimators using both a theoretical and a simulation study. The proposed family of estimators was found to be more efficient than the existing estimators.

The paper produces some new modified forms of the ratio estimators using the auxiliary information. The large sample properties, that is, the bias and mean squared error up to the first order of approximation are determined. The comparison is made with other existing estimators by using an applied data. It has been observed that the proposed estimators have a fewer mean squared error and leads to the efficient results as compared to the classical ratio estimator, Sisodia and Dwivedi, Singh and Kakran, Upadhyaya and Singh estimators. [ABSTRACT FROM AUTHOR]

In this paper, a ratio estimator is proposed for path sampling, which is a cost-effective sampling design for spatial population where population paths are created and sampled. The efficiencies of the ratio estimator and the former unbiased estimator for path sampling are compared by simulation study, where the result shows that the ratio estimator is more efficient than the existing unbiased estimator in path sampling. [ABSTRACT FROM AUTHOR]

Improved chain-ratio estimators for the population mean based on two-phase sampling are proposed when the study variable and two auxiliary variables comprise non-response. Auxiliary information is available for the first variable and not available for the second variable. Their biases and mean square errors are estimated under large sample approximation. Their efficiencies are compared with Hansen and Hurwitz's estimator, the ratio and regression estimators for a single auxiliary variable, and Singh and Kumar's estimators for two auxiliary variables. Empirical evaluations using both model-based and design-based simulations show that these estimators perform better than Hansen and Hurwitz's estimator, the ratio and the regression estimators, and Singh and Kumar's estimator. [ABSTRACT FROM AUTHOR]