Adaptive Cluster Sampling Design Research Articles

On Combining Ratio and Product Type Estimators For Estimation of Finite Population Mean In Adaptive Cluster Sampling Design

This article introduces a novel class of estimators and several new novel member estimators, combining the ratio and product forms, within the framework of Adaptive Cluster Sampling (ACS) design for estimating finite population mean. Specifically designed for rare or hidden clustered populations, the new novel estimators developed from the proposed class offer enhanced efficiency in estimation. To study the proposed class comprehensively, we derive expressions for the bias and Mean Squared Error (MSE) up to the first order of approximation. Through comprehensive simulation studies, we demonstrate the superior efficiency of the new developed estimators over several existing alternatives considered in this study.

Efficient Classes of Robust Ratio Type Estimators of Mean and Variance in Adaptive Cluster Sampling

This paper proposes two classes of robust ratio type estimators of finite population mean and two classes of robust ratio type estimators of finite population variance using a single auxiliary variable under the adaptive cluster sampling design. Seven robust ratio type estimators have been developed from each class. The generalized expressions of bias and mean square error for each class have been derived up to the first order of approximation. The exact expressions of bias and MSE for all the developed estimators have been presented. Using simulation studies conducted in R programming, the high efficiency of all the developed estimators over similar existing estimators in adaptive cluster sampling has been demonstrated. . KEYWORDS :Adaptive cluster sampling, Classes of robust ratio type estimators, Hidden clustered data, Estimation of mean, Estimation of variance.

Wider Classes of Estimators in Adaptive Cluster Sampling

Aims/ Objectives: Various efficient estimators using single and dual auxiliary variables with different functions including log and exponential have been developed in the SRSWOR design. Since the Adaptive cluster sampling (ACS) design is relatively new, estimators using functions like log and exponential with single and dual auxiliary variables have not been explored much. Therefore in this article, we propose two wider classes of estimators using single and dual auxiliary variables respectively so that the properties like bias and mean squared errors of various estimators using functions like log and exponential or any other function which belong to the proposed wider classes and have not been developed and studied yet would be known in advance. Formulae of the bias and mean squared error have been derived and presented. Further, since log type estimators have not been studied extensively in the ACS design we have developed new log type classes from each of the proposed wider classes and developed and studied some new log type member estimators. To examine the performance of these new developed log-type estimators over some competing estimators simulation studies have been conducted and all the estimators are further applied to a real data to estimate the average number of Mules in the Indian state of Assam. The studies show that the developed log-type estimators perform better.

Ratio-cum-product Type Estimators for Rare and Hidden Clustered Population.

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.

Some Efficient Exponential Ratio Type Estimators in Adaptive Cluster Sampling

In this paper three efficient exponential ratio type estimators of finite population mean in the Adaptive Cluster Sampling design have been proposed using one known auxiliary variable. The expressions of bias and mean squared error of the proposed estimators are derived up to the first order of approximation. A simulation study has been conducted on two different populations to examine the performance of the proposed estimator over similar existing estimators in the Adaptive Cluster Sampling design. The simulation study showed that the proposed estimators perform better than other related estimators discussed in this article.

Modelling Rare Events in an Adaptive Cluster Sampling Design with Heterogeneity among Networks and within the Network Units

Rare events population (φ) is hard-to-reach, sparsely distributed and clustered; an Adaptive Cluster Sampling (ACS) is the design to collect information from φ. Researchers and Policy Makers have modelled φ in ACS design with homogeneity assumptions. This study modelled φ with heterogeneity among networks and within the network units. Data from the International Institute of Tropical Agriculture on Culcasia Scandens, an understory plant and simulation were used to validate the model. Estimators for total and average number of rare events were derived and their statistical properties were examined. Bayesian Model was embedded in the designed ACS to develop the model for predicting the total number of rare events. Parameters α, β and λ were used in the model to control the expected number of grid cells with rare events, the conditional expected number of sub-network and expected number of rare events in each sub-network respectively. Markov Chain Monte-Carlo Algorithm with R and Winbugs software were used to estimated these parameters. The robustness of the model was examined and its Sensitivity Analysis was carried out. Diagnostic checks were done and the proposed model was compared with the existing model. The samples converged and represented the target posterior and the total number of rare events estimated lies within the 95% HPD credible interval. The derived estimators were unbiased, consistent and efficient. The model was criterion and inference robust with a good fit. The results revealed that rare event was best modelled under heterogeneity assumptions.

Modifications on re-scaling bootstrap for adaptive sampling

In complex survey design, the resampling method is often used for assessing the variability and confidence interval of non-linear estimators which is a function of several estimated means or totals. A well-known resampling method, called the re-scaling bootstrap technique was originated by Rao and Wu (1988). This article is an attempt to propose a re-scaling bootstrap technique in estimating the parameters of rare and clustered population for a complex survey design. Adaptive cluster sampling design is a probabilistic approach to reach out to the rare and clustered units. Thompson (1990) introduced this design. Chaudhuri (2000) extended this design for varying probability sampling. In practice, the final sample size of adaptive sampling may be exorbitantly large. From this realistic point of view, Chaudhuri, Bose, and Dihidar (2005) developed the size-constrained adaptive sampling design, in varying probability sampling. We first describe here, how this well-known re-scaling bootstrap technique may be employed for non-linear estimators of the population total, in the case of rare and clustered population. It has been found that there is a need to develop an alternative re-scaling bootstrap procedure to avoid complications in computation to cover Chaudhuri, Bose, and Dihidar (2005). A simulation study has been carried out to demonstrate the proposed methods.

Abundance and habitat associations of the globally endangered Giant NuthatchSitta magnain Southern Shan State, Myanmar

SummaryThe Giant NuthatchSitta magnais a globally endangered species presumed to be declining, for which basic parameters of population and habitat associations remain largely unquantified. We focused on Myanmar, which potentially constitutes ~30% of the Giant Nuthatch global range and yet lacks recently published records. Our objectives were to survey key potential Giant Nuthatch localities in, or near, historical locations in Southern Shan State, assess its population status, and quantify habitat associations. Preliminary locality surveys focused on four potential forest patches, assessed by walking approximately 40 km of trails. The species was found in only one of the four localities (Mt. Ashae Myin Anauk Myin [AMAM]), an 18 km2forest patch in Pindaya and Lawksawk Townships. Here, point counts and vegetation surveys were conducted at 46 locations using an adaptive cluster sampling design. N-mixture models were applied to estimate abundance and identify habitat variables correlated with abundance and detection probability. We also conducted a brief quantitative assessment of tree use and foraging behaviour during one breeding season. Our population estimate for AMAM was 56 individuals (95% CI 25–128) based on a sampled area of 3.25 km2. Abundance was positively associated with larger diameter trees, a higher proportion of pine and oak combined based on their total basal area, and negatively correlated with elevation. Foraging data suggested that Giant Nuthatch preferred to feed on trunks and large branches of larger diameter pines and Fagaceae trees. Based on the estimated population size, AMAM is probably a globally significant locality for Giant Nuthatch and the only confirmed locality in Myanmar since 1992 but is threatened by agricultural expansion. More detailed understanding of the habitat requirements of this endangered species and an assessment of its distribution at the landscape-level, especially in Shan State, would increase the precision of global population estimates.

Towards a robust baseline for long-term monitoring of Antarctic coastal benthos

The Southern Ocean represents one of the world regions most sensitive to warming and there is an urgent need for quantitative data to understand changes in coastal communities. This goal can be achieved through the establishment of permanent monitoring sites and robust sampling designs. In this study, we used an emerging, photogrammetry-based technique to simulate a pilot study and test the efficiency of different sampling schemes (Simple Random—SRS-, Systematic—SyS- and Strip—SS-) for estimating the abundances of megabenthic taxa. For taxa showing an aggregated distribution, we also applied an adaptive cluster sampling (ACS) design. In almost the totality of cases, the best accuracy of estimates was achieved with SyS combined with plots of 0.0625 m2. ACS design gave better performances but required a calibration of both the initial sample size and the threshold value to increase efficiency. The ‘one-size-fits-all’ 1 m2 plot size never emerged as the best in any sampling schemes, hence the previously published literature data can be biased. This study represents a fine-scale reference baseline for the study area and the simulations performed will be pivotal in establishing sound-monitoring programmes with sufficient statistical power to detect significative changes in the Antarctic benthos.

Generalized Exponential Estimator for the Estimation of Clustered Population Variance in Adaptive Cluster Sampling

In this paper, we proposed a generalized exponential estimator with two auxiliary variables for the estimation of highly clumped population variance under adaptive cluster sampling design. The expressions of approximate bias and minimum mean square error are derived. A family of exponential ratio and exponential product estimator is obtained by using different values of generalized and optimized constants. A numerical study is carried out on real and artificial populations to examine the performance of the proposed estimator over the competing estimators. Related results show that the proposed generalized exponential estimator is able to provide considerably better results over the competing estimators for the estimation of rare and highly clustered population variance.

Generalized estimator for the estimation of clustered population mean in adaptive cluster sampling

In many real-world survey situations, the use of auxiliary information together with the survey variable is very common phenomenon. The ratio and regression estimators are most commonly used estimation methods that incorporate the auxiliary information in various forms to improve the efficiency of the estimators. Adaptive cluster sampling is specifically developed for the estimation of rare and clustered population parameters and applied to a wide range of situations like, plants and animals of rare and endangered species, uneven minerals and drug users. In this paper, we proposed a generalized estimator with a single auxiliary variable for the estimation of highly clumped population mean under adaptive cluster sampling design. The proposed estimator utilizes the different combination of known parameters of the auxiliary variable. The expressions of approximate bias and mean square error are derived up to the first-order approximation. The Proposed estimator is found to be more efficient than the estimators proposed under certain conditions. A numerical study is carried out on real and artificial bivariate populations to support the performance of the proposed estimator over the above-mentioned estimators.

Multistage and adaptive sampling protocols combined with near-infrared spectral sensors for automated monitoring of raw materials in bulk

A near-infrared (NIR) spectroscopy-based real-time monitoring system is proposed to sample and analyse agro-industrial raw materials transported in bulk in a single stage, easing and optimising the evaluation process of incoming lots at reception of agri-food plants. NIR analysis allows rapid and cost-effective analytical results to be obtained, and hence to rethink current sampling protocols. For this purpose, multistage and adaptive sampling designs were tested in this paper, which have been reported (in soil science and ecology) to be more flexible and efficient than conventional strategies to study patterns of clustering or patchiness, which can be the result of natural phenomena. The additional spatial information provided by NIR has also been exploited, using geostatistical analysis to model the spatial pattern of key analytical constituents in Processed Animal Proteins (PAPs). This study addresses the assessment of two kinds of quality/safety issues in PAP lots – moisture accumulation and cross-contamination. After a simulation study, qualitative and quantitative analyses were carried out to make a performance comparison between sampling designs. Results show that sampling densities below 10–15% demonstrated higher estimation errors, failing to represent the actual spatial patterns, while a stratified adaptive cluster sampling design achieved the best performance.

Variance estimation in adaptive cluster sampling

In this paper, a class of variance estimator is proposed of a finite population variance under an adaptive cluster sampling design in the presence of information on an auxiliary variable. We obtain expressions for the mean square error and bias for the developed estimators and their performance is evaluated on a Poisson clustered process and a real data set. The simulation study evaluates the efficiency of the suggested estimators for an adaptive cluster sampling (ACS) design and the Isaki (1983) estimator of the variance for SRSWOR over the sample variance for SRSWOR.

Negative adaptive cluster sampling

The adaptive cluster sampling (ACS) design has been discussed in Chap. 10. Although the ACS design is found appropriate for sampling from a rare and clustered population, it suffers from the drawback of losing control of the final sample size. Several suggestions have been made by the different researchers for limiting this final sample size of the adaptive cluster sample. For instance, Salehi and Seber (1997a, b) suggested a two-stage sampling design in which primary units are selected using a conventional design and secondary units within the selected primary units are sub-sampled using ACS. Brown (1994) proposed a design in which initial sample is selected sequentially until the final sample size reaches a specified value.

Two-Stage Negative Adaptive Cluster Sampling

If the population is rare and clustered, then simple random sampling gives a poor estimate of the population total. For such type of populations, adaptive cluster sampling is useful. But it loses control on the final sample size. Hence, the cost of sampling increases substantially. To overcome this problem, the surveyors often use auxiliary information which is easy to obtain and inexpensive. An attempt is made through the auxiliary information to control the final sample size. In this article, we have proposed two-stage negative adaptive cluster sampling design. It is a new design, which is a combination of two-stage sampling and negative adaptive cluster sampling designs. In this design, we consider an auxiliary variable which is highly negatively correlated with the variable of interest and auxiliary information is completely known. In the first stage of this design, an initial random sample is drawn by using the auxiliary information. Further, using Thompson’s (J Am Stat Assoc 85:1050–1059, 1990) adaptive procedure networks in the population are discovered. These networks serve as the primary-stage units (PSUs). In the second stage, random samples of unequal sizes are drawn from the PSUs to get the secondary-stage units (SSUs). The values of the auxiliary variable and the variable of interest are recorded for these SSUs. Regression estimator is proposed to estimate the population total of the variable of interest. A new estimator, Composite Horwitz–Thompson (CHT)-type estimator, is also proposed. It is based on only the information on the variable of interest. Variances of the above two estimators along with their unbiased estimators are derived. Using this proposed methodology, sample survey was conducted at Western Ghat of Maharashtra, India. The comparison of the performance of these estimators and methodology is presented and compared with other existing methods. The cost–benefit analysis is given.

Two Stage Inverse Adaptive Cluster Sampling With Stopping Rule Depends upon the Size of Cluster

When the population is rare and patchy, the traditional sampling designs provide the poor estimate of the population mean/total. In such situations adaptive sampling is useful. Also, the population is spread over a large geographical area, then it is divided into clusters and random sample of clusters is selected. The clusters so selected form a set of primary stage units (PSU’s). Further a random sample of units is selected from the selected clusters. They form a set of secondary stage units (SSU’s).This method is called as two-stage cluster sampling. In this article, we have proposed a new sampling design which is a combination of two stage inverse cluster sampling and adaptive cluster sampling designs (ACS). At the first stage, population is divided into non-overlapping clusters and a random sample of pre-fixed number of clusters is selected from these clusters. At the second stage, an initial sample of a fixed size is selected from each of these selected clusters. Further number of units satisfying some pre-determined condition (number of successes) is decided for each cluster. This number of successes depends upon the size of the cluster. If the initial sample from a cluster includes the required number of successes (non-zero units) then sampling is stopped and adaptation of neighbors is made. Otherwise sampling is continued till either the required number of successes are obtained or a pre-fixed upper bound for the number of units to be sampled from a cluster is attained. The estimator of population total at each stage is proposed by using Rao-Blackwellization procedure. Monte-Carlo study is presented for the sample survey of Western Ghat, India, to verify the efficiency of proposed design.

Rare and clustered population estimation using the adaptive cluster sampling with some robust measures

ABSTRACTThe use of robust measures helps to increase the precision of the estimators, especially for the estimation of extremely skewed distributions. In this article, a generalized ratio estimator is proposed by using some robust measures with single auxiliary variable under the adaptive cluster sampling (ACS) design. We have incorporated tri-mean (TM), mid-range (MR) and Hodges-Lehman (HL) of the auxiliary variable as robust measures together with some conventional measures. The expressions of bias and mean square error (MSE) of the proposed generalized ratio estimator are derived. Two types of numerical study have been conducted using artificial clustered population and real data application to examine the performance of the proposed estimator over the usual mean per unit estimator under simple random sampling (SRS). Related results of the simulation study show that the proposed estimators provide better estimation results on both real and artificial population over the competing estimators.

Generalized variance estimators in adaptive cluster sampling using single auxiliary variable

This study presents generalized variance estimators utilizing the information on single auxiliary variable in adaptive cluster sampling for finite population variance. The expressions for mean square errors and biases for proposed variance estimators are obtained. The result of simulation study presents that the suggested variance estimators for adaptive cluster sampling (ACS) design are most efficient for population variance as compare to Isaki (1983) variance estimator for SRSWOR.

Using adaptive line-transect sampling in airborne geophysics studies

ABSTRACTWe introduce a design that combines elements from distance and adaptive cluster sampling designs. We propose a line-transect sampling method, where the sample-strips are selected by unequal selection probabilities, detectability of clusters is assumed imperfect and detectability of sample units belonging to each detected cluster is assumed perfect. Here, the application of distance sampling is broaden to airborne geophysics studies. We introduce efficient estimators for this new sample design. Also, we conduct two simulation studies. One of the populations is Sar Cheshmeh Copper mine with data from an airborne geophysics study and the other is an artificial population.

Adaptive cluster double sampling with post stratification with application to an epiphytic lichen community

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.