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In this paper, a ratio-product estimator for estimating the population mean of the study variable based on the population coefficient of skewness of the auxiliary variable is suggested in stratified double sampling. Asymptotic optimum estimator and its approximate bias and variance expressions are derived. Properties of the suggested estimator are studied with some known existing estimators identified as special members of this class of estimators. Analytical and numerical investigations showed that the suggested estimator is more efficient than the conventional regression estimator of mean in stratified double sampling and existing estimators of its class in stratified double sampling. Analysis and evaluation are presented.

Double sampling for stratification (2SS) is a sampling design that is widely used for forest inventories. We present the mathematical derivation of two appropriate variance estimators for mean growth from repeated 2SS with updated stratification on each measurement occasion. Both estimators account for substratification based on the transition of sampling units among the strata due to the updated allocation. For the first estimator, sizes of the substrata were estimated from the second-phase sample (sample plots), whereas the respective sizes in the second variance estimator relied on the larger first-phase sample. The estimators were empirically compared with a modified version of Cochran’s well-known 2SS variance estimator that ignores substratification. This was done by performing bootstrap resampling on data from two German forest districts. The major findings were as follows: (i) accounting for substratification, as implemented in both new estimators, has substantial impact in terms of significantly smaller variance estimates and bias compared with the estimator without substratification, and (ii) the second estimator with substrata sizes being estimated from the first-phase sample shows a smaller bias than the first estimator.

Count data arising in various fields of applications are often under‐reported. Ignoring undercount naturally leads to biased estimators and inaccurate confidence intervals. In the presence of undercount, in this paper, we develop likelihood‐based methodologies for estimation of mean using validation data. The asymptotic distributions of the competing estimators of the mean are derived. The impact of ignoring undercount on the coverage and length of the confidence intervals is investigated using extensive numerical studies. Finally an analysis of heat mortality data is presented.

The present paper deals with the problem of estimating the product of two population means using the information of auxiliary character under double sampling the non-respondents. Two different cases are considered for suggesting the estimators to estimate the product of two population means. The bias and mean square errors are obtained up to the first order of approximation, and the conditions for obtaining the minimum mean square errors of suggested estimators are derived. Theoretical and empirical studies with real data sets published by the Government of India are carried out to demonstrate the efficiency of the proposed estimators over the relevant estimators used in practice.

In this study, we suggest a family of ratio estimators for the population mean parameter using various robust regression techniques. These robust regressions techniques are Huber MM, LTS, and LMS estimates. We evaluate the performance of estimators in terms of the mean square error (MSE), and we compare the efficiency of our proposed robust-regression-ratio-type estimators with existing estimators under the optimal conditions. These comparisons show that our robust ratio-type estimators give more efficient results than the existing estimators under double sampling. In addition, the simulation and the empirical studies based on a data set that includes unusual observations show that our proposed estimators have a lower MSE than the existing estimators.

It is costly to collect the household- and individual-level data that underlies official estimates of poverty and health. For this reason, developing countries often do not have the budget to update their estimates of poverty and health regularly, even though these estimates are most needed there. One way to reduce the financial burden is to substitute some of the real data with predicted data. An approach referred to as double sampling collects the expensive outcome variable for a sub-sample only while collecting the covariates used for prediction for the full sample. The objective of this study is to determine if this would indeed allow for realizing meaningful reductions in financial costs while preserving statistical precision. The study does this using analytical calculations that allow for considering a wide range of parameter values that are plausible to real applications. The benefits of using double sampling are found to be modest. There are circumstances for which the gains can be more substantial, but the study conjectures that these denote the exceptions rather than the rule. The recommendation is to rely on real data whenever there is a need for new data, and use the prediction estimator to leverage existing data.

Chain-ratio estimators are often used to improve the efficiency of the estimation of the population total or the mean using two auxiliary variables, available in two different phases. An improved c...

A flexible scrambled response model using a randomization device for quantitative sensitive data is used to evaluate the protection of respondents’ privacy. A double-sampling regression-cum-exponen...

This manuscript presents the process for estimating the mean number of individuals having rare sensitive characteristic when population units are heterogeneous with and without prior information on the supplementary (unrelated rare non-sensitive) characteristic. The rare stigmatized parameter is estimated using an ameliorated two-stage randomized response model under stratified sampling and stratified double sampling schemes. The properties of the suggested estimators have been discussed under random, proportional and optimal allocations of sample from different strata. The proposed estimators perform better over some contemporary competent estimators for similar situations which have been shown through empirical studies.

Shabbir (Commun Stat Theory Methods 47(1):92–101, 2018) suggested a new difference type estimator of finite population mean in stratified double sampling using the ranks of two auxiliary variables as additional information. In this paper, on applying Searls’s (J Am Stat Assoc 59:1225–1226, 1964) approach to Shabbir’s (2018) estimator, we propose an improved estimator of population mean. The expressions of bias and mean square error of the proposed estimator have been obtained, up to first order of approximation. Theoretical and numerical comparisons of the mean square error of the proposed estimator with that of various existing estimators have been made. It is observed that proposed estimator always performs better than Shabbir’s (2018) estimator and also better than most of the other various existing estimators in the literature of survey sampling.

This article deals with the problems of efficient estimation of population variance in two-phase (double) sampling. Using information on two auxiliary variables, a class of chain exponential to regression type estimators has been proposed and its properties are studied under two different structures of two-phase sampling. Superiority of suggested class of estimators over some existing ones is established through numerical illustrations. Suitable recommendations to the survey statistician are also made.

This paper addresses the problem of estimating the population variance S2y of the study variable y using auxiliary information in sample surveys. We have suggested a class of estimators of the population variance S2y of the study variable y when the population variance S2x of the auxiliary variable x is known. Asymptotic expressions of bias and mean squared error (MSE) of the proposed class of estimators have been obtained. Asymptotic optimum estimators in the proposed class of estimators have also been identified along with its MSE formula. A comparison has been provided. We have further provided the double sampling version of the proposed class of estimators. The properties of the double sampling version have been provided under large sample approximation. In addition, we support the present study with aid of a numerical illustration.

This paper suggests a stratified Kuk model to estimate the proportion of sensitive attributes of a population composed by a number of strata; this is undertaken by applying stratified sampling to the adjusted Kuk model. The paper estimates sensitive parameters when the size of the stratum is known by taking proportional and optimal allocation methods into account and then extends to the case of an unknown stratum size, estimating sensitive parameters by applying stratified double sampling and checking the two allocation methods. Finally, the paper compares the efficiency of the proposed model to that of the Su, Sedory and Singh model and the adjusted Kuk model in terms of the estimator variance. Este trabajo propone un modelo Kuk estratificado para estimar la proporción de atributos sensibles de una población compuesta por varios estratos mediante la aplicación de un muestreo estratificado al modelo Kuk ajustado. El trabajo estima parámetros sensibles en el caso en que el tamaño del estrato es conocido mediante la adopción de métodos de asignación proporcionales y óptimos, y se extiende al caso de un tamaño de estrato desconocido, estimando parámetros sensibles mediante la aplicación de un doble muestreo estratificado y la comprobación de los dos métodos de asignación. Por último, el trabajo compara la eficiencia del modelo propuesto a la del modelo de Su, Sedory y Singh y el modelo Kuk ajustado en términos de la varianza del estimador.

Non-ignorable dropout is common in studies with long follow-up time, and it can bias study results unless handled carefully in the study design and the statistical analysis. A double-sampling design allocates additional resources to pursue a subsample of the dropouts and find out their outcomes, which can address potential biases due to non-ignorable dropout. It is desirable to construct semiparametric estimators for the double-sampling design because of their robustness properties. However, obtaining such semiparametric estimators remains a challenge due to the requirement of the analytic form of the efficient influence function (EIF), the derivation of which can be ad hoc and difficult for the double-sampling design. Recent work has shown how the derivation of EIF can be made deductive and computerizable using the functional derivative representation of the EIF in nonparametric models. This approach, however, requires deriving the mixture of a continuous distribution and a point mass, which can itself be challenging for complicated problems such as the double-sampling design. We propose semiparametric estimators for the survival probability in double-sampling designs by generalizing the deductive and computerizable estimation approach. In particular, we propose to build the semiparametric estimators based on a discretized support structure, which approximates the possibly continuous observed data distribution and circumvents the derivation of the mixture distribution. Our approach is deductive in the sense that it is expected to produce semiparametric locally efficient estimators within finite steps without knowledge of the EIF. We apply the proposed estimators to estimating the mortality rate in a double-sampling design component of the President’s Emergency Plan for AIDS Relief (PEPFAR) program. We evaluate the impact of double-sampling selection criteria on the mortality rate estimates. Simulation studies are conducted to evaluate the robustness of the proposed estimators.

We suggested the class of estimators of the population mean with its bias and mean square error. It has been shown that the suggested class is more efficient than the usual unbiased, ratio, product and regression estimators and estimators due to Bahl and Tuteja (1991), Singh et al. (2009), and Upadhyaya et al. (2011). In addition an empirical study also carried out to and founded that the members of suggested family also have improvement over Grover and Kaur (2011) and Shabbir and Gupta (2011) classes. Two-phase (double) sampling version of the proposed class was also given.

The aim of the study is to suggest a difference-cum-ratio type of median estimator for finite population median using two-auxiliary variables in double sampling. Using simple random sampling without-replacement scheme (SRSWOR) the estimated mean square error (MSE) and BIAS are computed for the new suggested median estimator. The suggested median estimator has a smaller MSE than all other median estimators currently in practice, showing a valid contribution to the literature. In addition some members of the suggested estimator and theoretical comparison of MSE are also computed. Finally, the numerical and graphical comparison of percent relative efficiency (PRE) is also computed for five different real data sets.

The implementation of an adaptive cluster sampling design often becomes logistically challenging because variation in the final sampling effort introduces uncertainty in survey planning. To overcome this drawback, an inexpensive and easy to measure auxiliary variable could be used in a two-phase survey strategy, called adaptive cluster double sampling (Felix-Medina and Thompson in Biometrika 91:877–891, 2004). In this paper, a two-phase sampling strategy is proposed which combines the idea of adaptive cluster double sampling with the principle of post-stratification. In the first-phase an adaptive cluster sample is selected by means of an inexpensive auxiliary variable. Networks from the first phase sampling are then post-stratified according to their size. In the second-phase, the network structure is used to select a subsample of units by means of stratified random sampling. The proposed sampling strategy employs stratification without requiring an a priori delineation of the strata. Indeed, the strata sizes are estimated in the course of the two-phase sampling process. Therefore, it is suitable for situations where stratification is suspected to be efficient but strata cannot be easily delineated in advance. In this framework, a new type of estimator for the population mean which mimics the stratified sampling mean estimator and an estimator of the sampling variance are proposed. The results of a simulation study confirm, as expected, that the use of post-stratification leads to gain in precision for the estimator. The proposed sampling strategy is applied for targeting an epiphytic lichen community Lobarion pulmonariae in a forest area of the Northern Apennines (N-Italy), characterized by several species of conservation concern.

In this paper, we have suggested the families of estimators for estimating the finite population variance using auxiliary character under incomplete information due to non-response. The asymptotic expressions of bias and mean square error of the proposed families of estimators are obtained and their properties are studied. Theoretical and empirical studies are performed to show the relative performance of the suggested families of estimators.

Dash and Mishra [1] suggested an improved class of estimators without defining the optimum estimator. However, they gave the wrong Taylor’s series expression of their class of estimator and their minimum mean squared error expressions are also incorrect. Here we show that Ahmed et al.’s [2] class of chain estimators is more efficient than Dash and Mishra’s [1], with minimum mean squared error.

In this paper, we consider the problem of estimation of population mean of a study variable by making use of first-phase sample mean and first-phase sample median of the auxiliary variable at the estimation stage. The proposed new estimator of the population mean is compared to the sample mean estimator, ratio estimator and the difference type estimator for the fixed cost of the survey by using the concept of two-phase sampling. The magnitude of the relative efficiency of the proposed new estimator has been investigated through simulation study.

This paper discusses the problem of estimation of finite population mean in double sampling for stratification. In fact, ratio and product type exponential estimators of population mean are proposed in double sampling for stratification. The biases and mean squared errors of proposed estimators are obtained upto the first degree of approximation. The proposed estimators have been compared with usual unbiased estimator, ratio and product estimators in double sampling for stratification. To judge the performance of the proposed estimators an empirical study has been carried out.

Detectability issues create uncertainty in field surveys of animal and plant populations. Detectability correction is one method employed to deal with this problem when there is reasonable certainty that detectability is roughly constant with time or in different areas. Two new reduced-variance estimators of detectability are introduced and evaluated for the case of using a detectability correction for new areas that are surveyed only once. The new estimates are unbiased or nearly unbiased and produce population estimates with smaller variance than the Lincoln–Petersen estimate.

This paper presents exponential ratio and product estimators for estimating finite population mean using auxiliary information in double sampling and analyzes their properties. These estimators are compared for their precision with simple mean per unit, usual double sampling ratio and product estimators. An empirical study is also carried out to judge the merits of the suggested estimators.

For a current inventory using double sampling for stratification with a reduced second-phase sample size, compared with a previous inventory, we develop a three-phase sampling procedure that exploits plot data from the previous inventory or their updates based on a growth model to increase precision. The three-phase procedure combines double sampling for stratification with a two-phase regression estimator within strata. We consider sampling from an infinite population in the first phase. The combined estimator is tested in a case study using data from two consecutive inventories in four State Forest Districts in Lower Saxony, Germany. Data from a reduced number of sample plots from the second occasion are combined with (1) volumes from the first occasion or (2) growth simulations on the sample plots from the first occasion. The data from the previous inventory or their updates serve as the auxiliary variable for the regression estimator of the strata means of the target variable. This case study indicates a remarkable increase in precision and thereby an enormous cost-saving potential for reduced intermediate inventories in a periodic inventory design with both types of auxiliary variables. peerReviewed

This paper defines a general procedure for estimating the population mean of the study variate based on double sampling for stratification in presence of multi-auxiliary information. Classes of combined and separate estimators have been suggested and their properties are studied under large sample approximation. A class of unstratified double sampling estimators is also proposed with its properties. Asymptotic optimum estimators in the classes are identified with their approximate variance formulae. Further the proposed classes of estimators are compared with the corresponding class of estimators based on un-stratified double sampling. All findings are encouraging and support the soundness of the proposed procedure for mean estimation.

Double-sampling designs are commonly used in real applications when it is infeasible to collect exact measurements on all variables of interest. Two samples, a primary sample on proxy measures and a validation subsample on exact measures, are available in these designs. We assume that the validation sample is drawn from the primary sample by the Bernoulli sampling with equal selection probability. An empirical likelihood based approach is proposed to estimate the parameters of interest. By allowing the number of constraints to grow as the sample size goes to infinity, the resulting maximum empirical likelihood estimator is asymptotically normal and its limiting variance–covariance matrix reaches the semiparametric efficiency bound. Moreover, the Wilks-type result of convergence to chi-squared distribution for the empirical likelihood ratio based test is established. Some simulation studies are carried out to assess the finite sample performances of the new approach.

This paper studies nonparametric estimation of the regression function with surrogate outcome data under double-sampling designs, where a proxy response is observed for the full sample and the true response is observed on a validation set. A new estimation approach is proposed for estimating the regression function. The authors first estimate the regression function with a kernel smoother based on the validation subsample, and then improve the estimation by utilizing the information on the incomplete observations from the non-validation subsample and the surrogate of response from the full sample. Asymptotic normality of the proposed estimator is derived. The effectiveness of the proposed method is demonstrated via simulations.

This article presents the calibration procedure of the two-phase randomized response (RR) technique for surveying the sensitive characteristic. When the sampling scheme is two-phase or double sampling, auxiliary information known from the entire population can be used, but the auxiliary information should be information available from both the first and second phases of the sample. If there is auxiliary information available from both the first and second phases, then we can improve the ordinary two-phase RR estimator by incorporating this information in the estimation procedure. In this article, we used the new two-step Newton's method for computing unknown constants in the calibration procedure and compared the efficiency of the proposed estimator through some numerical study.

In this study, we compare the efficiency of double sampling using point sampling and fixed-area plots for sawtimber volume estimates in a mixed-hardwood, oak-dominated stand. Multiple sample sizes and combinations were evaluated to determine optimum double-sample ratios. Results indicatedthat double, point-sampling schemes are more efficient in terms of field time and sampling errors than double-sampling schemes incorporating fixed-area plots. Data suggested that the most efficient ratio of measured and nonmeasured points with double sampling varies on the basis of the nonmeasuredvariable used and desired SE percentage levels for the inventory.

In this article, we introduce minimum divergence estimators of parameters of a binary response model when data are subject to false-positive misclassification and obtained using a double-sampling plan. Under this set up, the problem of goodness-of-fit is considered and divergence-based confidence intervals (CIs) for a population proportion parameter are derived. A simulation experiment is carried out to compare the coverage probabilities of the new CIs. An application to real data is also given.

In this paper we have suggested a double sampling version of Sahai (10) estimator using simple random sampling without replacement (SRSWOR) at both phases and its properties are studied. The estimator is also compared with simple mean per unit for a given cost of the survey. An empirical study is carried out to demonstrate the performance of suggested estimator over usual estimators.

The paper proposes a class of dual to ratio estimators for estimating the mean of finite population, for double sampling.

Double sampling scheme is used when cheap auxiliary variables may be measured to improve the estimation of a finite population parameter. Several estimators for population mean, ratio of means and variance are available, when two dependent samples are drawn. However, there are few proposals for the case of independent samples. In this paper both cases of dependent and independent samples are dealt with. A general approach for estimating a finite population parameter is given, showing that all the proposed estimators are particular cases of the same general class. The minimum variance bound for any estimator in this class is provided (at the first order of approximation). Furthermore, an optimal estimator which reaches this minimum is found.

This paper puts forward an improved channel parameter estimator based on the level crossing rate (LCR) computation and double sampling rate (DSR) signal processing, where the appropriate sampling rate is studied by the numerical computation. Subsequently, by exploiting the selected sampling rate, we can estimate both the Doppler shift and the signal-to-noise ratio (SNR) with a high accuracy. Extensive simulations explicitly show a good performance for the proposed algorithm.

This paper proposes a general class of estimators for estimating the median in double sampling. The position estimator, stratification estimator and regression type estimator attain the minimum variance of the general class of estimators. The optimum values of the first-phase and second-phase sample sizes are also obtained for the fixed cost and the fixed variance cases. An empirical study examines the performance of the double sampling strategies for median estimation. Finally, an extension of the methods of Chen & Qin (1993) and Kuk & Mak (1994) is considered for the double sampling strategy.

Given that we know the population mean of an additional auxiliary variable z, we formulate a class of estimators for the finite population mean when the population mean of the main auxiliary variable x is unknown using a double sampling procedure. The class covers a wide range of estimators and acts as a complementary in a certain sense to the class suggested by Sahoo and Sahoo (1993).

The chain type estimators for population mean using auxiliary and additional auxiliary variables using double sampling scheme have been proposed and their properties are studied. The proposed estimators are also found to more efficient than the relevant chain type estimators for population mean proposed by Chand [1] and Kiregyera [2,3]. An empirical study has been given in the support of the proposed estimators.

This paper presents a class of predictive estimators for two stage sampling with unequal first and second stage units to the case where information on auxiliary character is not available. A double sampling procedure is proposed as alternative under such a situation. The proposed class consists of mainly two estimators namely ratio and regression. The mean square error (MSE) and minimum mean square of this class have been derived. In addition, we support these theoretical results by an empirical study.

This paper explore the need for exploiting auxiliary variables in sample survey and utilizing asymptotically optimum estimator in double sampling to increase the efficiency of estimators. The study proposed two types of estimators with two auxiliary variables for two phase sampling when there is no information about auxiliary variables at population level. The expressions for the Mean Squared Error (MSE) of the proposed estimators were derived to the first order of approximation. An empirical comparative approach of the minimum variances and percent relative efficiency were adopted to study the efficiency of the proposed and existing estimators. It was established that, the proposed estimators performed more efficiently than the mean per unit estimator and other previous estimators that don’t use auxiliary variable and that are not asymptotically optimum. Also, it was established that estimators that are asymptotically optimum that utilized single auxiliary variable are more efficient than those that are not asymptotically optimum with two auxiliary variables.

An attempt has been mads to suggest some estimators for population mean in double sampling with two auxiliary variables., alternative to the usual regression estimator. When the experimenter has partial Information about the mean of the auxiliary variable or variables, preliminary test estimators can be used. The bias, mean square error, relative efficiency and optimum allocation of sample sizes are obtained for the suggested estimators.

An approximation to the variances of the regression and mean of ratios estimators for double sampling is presented that can be used to determine how many basal area points are needed to augment an existing inventory to achieve a desired precision. The approximation may also be used to determine the effective regular sample size to achieve equal precision to a double sample.

The Theory of double sampling as proposed by Neyman (1938) and subsequently used for successive sampling by Jesson (1942), Yates (1960), Patterson (1950), Eckler (1955), Kuldroff (1963) and Tikkiwal (1960, 1967) has been explored to develop a general estimator which can be used for estimation of parameters such as mean, ratio or double ratio. A simple case of sampling on two occasions has only been considered but the logic can easily be extended for more than two occasions. The results show that the generalised estimator will be very useful for the applied statisticians.

Formulas are derived for determining the total number of sample points and the number of volume points for a point, double sample with a ratio of means estimator to replace a point sample and achieve the same variance. A minimum ratio of the cost of measuring volume to the cost of measuring basal area at a point is determined for which the point, double sample will be less costly, in terms of time required to measure points, than the point sample.

Several estimators for estimating the mean of a principal variable are proposed based on double sampling for stratification (DSS) and multivariate auxiliary information. The general properties of the proposed estimators are studied, search for optimum estimators is made and the proposed estimators are compared with the corresponding estimators based on unstratified double sampling (USDS).