Adaptive Cluster Sampling 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.

Adaptive sampling in ecology: Key challenges and future opportunities

Abstract Traditional ecological monitoring employs fixed designs, which do not vary over the survey duration. Adaptive sampling, whereby the data already collected informs a sampling design which changes over the course of the study, can provide a more optimal and flexible survey design but is little used in ecology. We aim to provide an introduction to adaptive sampling for ecologists. We review previous literature and highlight examples of both empirical adaptive approaches, such as adaptive cluster sampling, and more novel model‐based adaptive methods. To conceptualise the process of adaptive sampling we identify four key stages: choice of data, definition of a criterion, selection of new sampling occasions and sampling activity. We discuss each stage in turn and focus on the decisions ecologists need to consider in order to successfully implement an adaptive sampling strategy. We include a full walkthrough of an adaptive sampling example with code provided to demonstrate each step. Adaptive sampling has potential advantages to ecologists but so far has had limited uptake. We review key challenges and barriers to uptake and suggest potential ways forward. We hope our paper will both increase awareness of adaptive sampling methods and provide a useful resource for ecologists considering an adaptive survey design.

The impact of transformations on the performance of variance estimators of finite population under adaptive cluster sampling with application to ecological data

This paper aims to investigate the impact of transformed auxiliary variables on the performance of variance estimators of finite population under adaptive cluster sampling scheme. Further, the formulation of an efficient variance estimator of a finite population is also under consideration in this article. Specifically, we explore the gain in efficiency obtained through various transformations and define dominance space for each transformation. These dominance regions provide valuable insights into the circumstances under which one transformation prevails over another regarding precision and accuracy. The theoretical properties of the suggested estimators have been discussed along with the dominance region under each transformation. The bias and Mean Square Error (MSE) have been derived up to the first order of approximation. To evaluate and empirically validate our methodology, we conduct a numerical analysis using real-life ecological data of blue-winged teal. The finding reflects the superior performance of the suggested variance estimators over the competing estimators, thereby substantiating its importance in making informed decisions in real-world applications.

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

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

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.

Research on Adaptive Cluster Sampling Method Based on PPS

Research on Adaptive Cluster Sampling Method Based on PPS

Research on Adaptive Cluster Sampling Method based on PPS

This paper introduces the principle of PPS-based adaptive cluster sampling method and its modified HH estimator and HT estimator calculation method. It compares PPS-based adaptive cluster sampling method with SRS sampling and SRS-based adaptive group. The difference between the group sampling and the advantages and scope of the PPS adaptive cluster sampling method are analyzed. According to the case analysis, the relevant conclusions are drawn: 1) The adaptive cluster sampling method is more accurate than the SRS sampling; 2) SRS adaptive The HT estimator of the cluster sampling is more stable than the HH estimator; 3) The two estimators of the PPS adaptive cluster sampling method have little difference in the estimation of the population mean, but the HT estimator variance is smaller and more suitable; 4) PPS The HH estimator of adaptive cluster sampling is the same as the HH estimator of SRS adaptive cluster sampling, but the variance is larger and unstable.

A generalized class of estimators for the mean using multiauxiliary information in adaptive cluster sampling

This article addresses the problem of estimating the population mean of variable y using information from multiple auxiliary variables in adaptive cluster sampling. We define a class of estimators based on p(>1) auxiliary variables x 1 , x 2 , … . . , x p , derive bias and mean squared error expressions up to order n−1, and determine optimal conditions for minimizing mean squared error. Our findings demonstrate that the proposed estimators outperform the multiple linear regression estimator. We also identify several existing estimators as members of this class, including those introduced by Dryver and Chao (2007), Chutiman and Kumphon (2008), Chutiman (2013), Chaudhry (2014), Chaudhry and Hanif (2015), and Yadav et al. (2016). Furthermore, we obtain the correct values of constants “a” and “b” for the Chaudhry and Hanif (2015) estimator, leading to an accurate expression for its minimum mean squared error. To assess the performance of these estimators, we conduct a simulation study.

Two Phase Adaptive Cluster Sampling under Transformed Population Approach

Two Phase Adaptive Cluster Sampling under Transformed Population Approach

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.

Generating and validating cluster sampling matrices for model-free factor screening

Morris’ elementary effect-based screening (MM) has been widely used in a variety of domains to identify a few important factors among many possible ones. In MM, cluster sampling offers substantial computational savings over non-cluster sampling, but it remains a challenge to construct a cluster sampling matrix that generates any particular number of elementary effects for each factor. In this paper, we thoroughly address this issue. We uncover the mathematical association between distinct block sampling matrices within the complete cluster sampling matrix, by introducing a “dummy” sub-block matrix. By leveraging this property, we propose an easy-to-implement adaptive cluster sampling (ACS) method that is capable of identifying the appropriate sub-block sampling matrix to use. Its advantage over existing brute-force methods is that it can provide easy-to-obtain cluster sampling matrices, and it can be applied to computational model with any number of factors given a prior. We demonstrate the attractive properties of ACS using analytical proofs and simulation experiments. We show the robustness of ACS via a real-world case study. Our code for the algorithm is available online.

Adaptive cluster sampling based on balanced sampling plan excluding contiguous units

The method of adaptive cluster sampling (ACS) is useful for the surveys when the characteristic of interest is sparsely distributed but highly aggregated. In ACS, the initial sample is selected by simple random sampling (SRS). The final sample is obtained by adapting the nearby units which satisfy the pre-specified condition. This sampling can further be improved when the appropriate control is imposed to select the initial sample. In this article, Balanced Sampling plan Excluding Contiguous units (BSEC plan) has been used to select the initial sample for estimating population mean in ACS. The purpose is to ignore non preferred or contiguous units and include more preferred units in the final sample. The unbiased estimators of population mean based on the initial sample and modified Hansen-Hurwitz (HH) type estimators are discussed. It has been illustrated theoretically and empirically that the modified HH type estimator based on BSEC plan is more precise than that based on SRS. The proposed method provides the opportunity to select the non contiguous units in initial sample, which makes the design more informative and efficient in comparison to ACS. The proposed design may be helpful in improving the ACS estimates in many real-life situations.

An Application of Adaptive Cluster Sampling to Surveying Informal Businesses

Abstract Informal business activity is ubiquitous around the world, but it is nearly always uncaptured by administrative data, registries, or commercial sources. For this reason, there are rarely adequate sampling frames available for survey implementers wishing to measure the activity and characteristics of the sector. This article applies a well-established sampling method for rare and/or clustered populations, Adaptive Cluster Sampling (ACS), to a novel population of informal businesses. Generally, it shows that efficiency gains through the application of ACS, when compared to Simple Random Sampling (SRS), are large, particularly at higher levels of fieldwork effort. In particular, ACS efficiency gains over SRS remain sizable at higher values of initial starting samples, but with comparatively high expansion thresholds, which can reduce the fieldwork effort.

RATIO ESTIMATORS FOR POPULATION VARIANCE IN ADAPTIVE CLUSTER SAMPLING

To estimate the variance for rare and cluster population has been the main problemin survey sampling. Three ratio type estimators were proposed for population variance utilizing thesingle auxiliary variable assuming the transformed population for adaptive cluster sampling, inpresented study. The expressions for the mean square error and bias of the proposed estimator werederived. The proposed estimatorswere used to estimate the finite population variance in adaptivecluster sampling. The simulationswereperformedon a real life data to reveal and evaluate the efficiencyof the estimators. The results showed that the proposed exponential ratio estimator was more efficientcompared to the usual sample variance estimator and the proposed ratio type variance estimators inadaptive cluster sampling, assuming given conditions. Hence, exponential ratio estimators wererecommended to estimate the population variance in adaptive cluster sampling.

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.

Weighting estimation under bipartite incidence graph sampling

Bipartite incidence graph sampling provides a unified representation of many sampling situations for the purpose of estimation, including the existing unconventional sampling methods, such as indirect, network or adaptive cluster sampling, which are not originally described as graph problems. We develop a large class of design-based linear estimators, defined for the sample edges and subjected to a general condition of design unbiasedness. The class contains as special cases the classic Horvitz-Thompson estimator, as well as the other unbiased estimators in the literature of unconventional sampling, which can be traced back to Birnbaum et al. (1965). Our generalisation allows one to devise other unbiased estimators in future, thereby providing a potential of efficiency gains. Illustrations are given for adaptive cluster sampling, line-intercept sampling and simulated graphs.

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.

Use of calibration constraints and linear moments for variance estimation under stratified adaptive cluster sampling

Use of calibration constraints and linear moments for variance estimation under stratified adaptive cluster sampling

An adaptive clustering algorithm by neighbourhood search for large-scale data

Adaptive cluster sampling (ACS) is a sampling method relies on the neighbourhood search on a grid structure. It has an adaptive selection process of units and recursively added units reveal the batched individuals easily and quickly. In this paper, we propose a new clustering method called spatial adaptive clustering (SAC) based on the idea of ACS design. The SAC algorithm forms clusters based on neighbourhood search using grid structures and is able to detect noise points. The performance of the proposed algorithm is evaluated through comparison with the results from well-known density-based clustering approaches in the literature using real and artificial data sets. Computational results indicate that the proposed algorithm is effective in terms of external validation measures for clustering of arbitrary shaped data with noise. Additionally, the SAC algorithm is tested on artificial data sets of varying sizes for the runtime criterion. The results reveal that it also performs superbly for the objective of reducing the runtime.