Adaptive Cluster Sampling Research Articles

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.

Estimation of General Parameter Under Stratified Adaptive Cluster Sampling Based on Dual Use of Auxiliary Information

Auxiliary information is mostly used together with study variable to enhance efficiency of estimators for population mean, total and variance. Thompson introduced adaptive cluster sampling as an appropriate sampling scheme for rare and clustered populations. In present article, difference-type and difference-cum-exponential-ratio-type estimators are presented utilizing two auxiliary variables for estimation of general parameter under stratified adaptive cluster sampling. Proposed estimators utilize auxiliary information in terms of ranks, variances and means of auxiliary variables in $h^{th}$ stratum. Expressions for bias and mean square error of proposed estimators are derived using first order of approximation. Numerical study is conducted to evaluate the performance of proposed estimators.

Generalized estimator for the estimation of rare and clustered population variance in adaptive cluster sampling

ABSTRACTAdaptive cluster sampling (ACS) is considered to be the most suitable sampling design for the estimation of rare, hidden, clustered and hard-to-reach population units. The main characteristic of this design is that it may select more meaningful samples and provide more efficient estimates for the field investigator as compare to the other conventional sampling designs. In this paper, we proposed a generalized estimator with a single auxiliary variable for the estimation of rare, hidden and highly clustered population variance under ACS design. The expressions of approximate bias and mean square error are derived and the efficiency comparisons have been made with other existing estimators. A numerical study is carried out on a real population of aquatic birds together with an artificial population generated by Poisson cluster process. Related results of numerical study show that the proposed generalized variance estimator is able to provide considerably better results over the competing estimators.

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.

Generalized ratio-type and ratio-exponential-type estimators for population mean under modified Horvitz-Thompson estimator in adaptive cluster sampling

ABSTRACTIn the present article, we propose the generalized ratio-type and generalized ratio-exponential-type estimators for population mean in adaptive cluster sampling (ACS) under modified Horvitz-Thompson estimator. The proposed estimators utilize the auxiliary information in combination of conventional measures (coefficient of skewness, coefficient of variation, correlation coefficient, covariance, coefficient of kurtosis) and robust measures (tri-mean, Hodges-Lehmann, mid-range) to increase the efficiency of the estimators. Properties of the proposed estimators are discussed using the first order of approximation. The simulation study is conducted to evaluate the performances of the estimators. The results reveal that the proposed estimators are more efficient than competing estimators for population mean in ACS under both modified Hansen-Hurwitz and Horvitz-Thompson estimators.

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 adaptive cluster sampling based on ordered statistics

The estimation problem on sparsely distributed populations using adaptive cluster sampling (ACS) is discussed. In the first phase of ACS, two stage sampling is used in which primary and secondary sampling units are selected using simple random sampling without replacement. The idea of Thompson (1996) is introduced in order to choose an appropriate fixed value of pre-specified condition, which might represent the number of rare species, before conducting the survey by the use of order statistics. Different estimators of the population mean under the two possible schemes (open and closed boundaries of primary sampling units) are studied and the Rao-Blackwell theorem for improving these estimators is also used. Numerical illustrations, one on real life data and the other based on simulation study, are discussed for these two schemes. This design may be quite useful in environmental, forestry and other areas of research dealing with rare, endangered or threatened species.

Population status of endemic tree kokoleceran (Vatica bantamensis) in Ujung Kulon National Park, Indonesia

Abstract. Robiansyah I, Dodo, Hamidi A. 2019. Population status of endemic tree kokoleceran (Vatica bantamensis) in Ujung Kulon National Park, Indonesia. Biodiversitas 20: 296-302. Kokoleceran (Vatica bantamensis) is an endemic tree found only in Ujung Kulon National Park (UKNP), Banten, Indonesia, and is classified as Endangered by IUCN Red List. To develop effective conservation measures of threatened plants, current information on population status and distribution of the species is needed. Thus in the present study, a targeted survey of kokoleceran was conducted in UKNP aiming at mapping the distribution of the species, measuring current population size and structure, assessing the habitat preferences, and identifying threats to the species. Using a non-random adaptive cluster sampling, a total of 27 clusters harboring 280 individuals of kokoleceran was located, of which 20 % were in mature stage. All these individuals were only found in Mount Payung and its surrounding areas, and formed an inverse-J-shaped population structure pattern. The species was estimated to have an area of occupancy and extent of occurrence of 8 km2. The invasive langkap palm (Arenga obtusifolia, Arecaceae) was identified as the main threat for kokoleceran. Based on these results, kokoleceran appears to more than justify its conservation status of Critically Endangered B1ab(iii,v) +2ab(iii,v); C2a(ii).

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.

Estimation of rare and clustered population variance in adaptive cluster sampling

Many researchers used auxiliary information together with survey variable to improve the efficiency of population parameters like mean, variance, total and proportion. Ratio and regression estimation are the most commonly used methods that utilized auxiliary information in different ways to get the maximum benefits in the form of high precision of the estimators. Thompson first introduced the concept of Adaptive cluster sampling, which is an appropriate technique for collecting the samples from rare and clustered populations. In this article, a generalized exponential type estimator is proposed and its properties have been studied for the estimation of rare and highly clustered population variance using single auxiliary information. A numerical study is carried out on a real and artificial population to judge the performance of the proposed estimator over the competing estimators. It is shown that the proposed generalized exponential type estimator is more efficient than the adaptive and non adaptive estimators under conventional sampling design.

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.

SAMPLING PROCESSES FOR Carapa guianensis AUBL. IN THE AMAZON

ABSTRACT The objective of this study was to analyze the adaptive cluster sampling (ACS), simple random sampling (SRS) and systematic sampling (SS) processes to obtain the number of ha-1 trees of Carapa guianensis Aubl. in the Amazon. The data were obtained through 100% inventory and sampling simulations, considering a DBH ≥ 25 cm, a sampling intensity of 4%, a maximum error of 10% and plots of 0.09, 0.16 and 0.25 ha. The last two sizes were only used to analyze their effect on the ACS estimators. The processes were evaluated for accuracy, precision (E%) and confidence interval (CI), while the mean ha-1 of the processes were compared with that of the 100% inventory by the Z test. The ACS process showed no significant difference between its average ha-1 trees and the 100% inventory, and it was also the most accurate and the only one whose CI was true. However, it presented a final sample intensity 3.6 times greater than the simple and systematic random samplings, in addition to E% above 10%, which makes it unacceptable, legally, and economically unfeasible. The other processes had densities significantly higher than the 100% inventory, with sample intensities lower than ACS and E% lower than 10%, making them legally viable. The use of larger plots in the ACS implies larger clusters and a greater tendency to underestimate the number of trees, resulting in larger sample errors and less accuracy.

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.

A Class of Hartley-Ross-Type Estimators for Population Mean in Adaptive and Stratified Adaptive Cluster Sampling

In this article, we propose a class of Hartley-Ross-type unbiased estimators of finite population mean under adaptive cluster sampling and stratified adaptive cluster sampling. The estimators utilize information on known parameters of the auxiliary variable. The variances of proposed class of unbiased estimators are obtained up to first degree of approximation. Proposed estimators are more efficient than the usual mean estimator, ratio, and modified ratio estimators in adaptive cluster sampling and stratified adaptive cluster sampling under certain realistic conditions. Simulation study considering different populations is carried out to support the theoretical findings.

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.

K-step adaptive cluster sampling with Horvitz–Thompson estimator

Adaptive cluster sampling (ACS) has been widely used for data collection of environment and natural resources. However, the randomness of its final sample size often impedes the use of this method. To control the final sample sizes, in this study, a [Formula: see text]-step ACS based on Horvitz–Thompson (HT) estimator was developed and an unbiased estimator was derived. The [Formula: see text]-step ACS-HT was assessed first using a simulated example and then using a real survey for numbers of plants for three species that were characterized by clustered and patchily spatial distributions. The effectiveness of this sampling design method was assessed in comparison with ACS Hansen–Hurwitz (ACS-HH) and ACS-HT estimators, and [Formula: see text]-step ACS-HT estimator. The effectiveness of using different [Formula: see text]-step sizes was also compared. The results showed that [Formula: see text]-step ACS-HT estimator was most effective and ACS-HH was the least. Moreover, stable sample mean and variance estimates could be obtained after a certain number of steps, but depending on plant species. [Formula: see text]-step ACS without replacement was slightly more effective than that with replacement. In [Formula: see text]-step ACS, the variance estimate of one-step ACS is much larger than other [Formula: see text]-step ACS ([Formula: see text]), but it is smaller than ACS. This implies that [Formula: see text]-step ACS is more effective than traditional ACS, besides, the final sample size can be controlled easily in population with big clusters.

Fujian cypress and two other threatened tree species in three conservation zones of a nature reserve in north-western Vietnam

BackgroundFujian cypress (Fokienia hodginsii) is a highly valued but endangered tree species. The Ta Xua Nature Reserve in Vietnam is one of its main conservation centers. This nature reserve consists of a fully protected core zone, a buffer zone in which low intensity forest use is permitted, and a forest restoration zone in which forest regenerates after shifting cultivation.MethodsThe community and population status of F. hodginsii and two other threatened tree species (Aglaia spectabilis and Quercus platycalyx) were assessed across the three conservation zones. Based on 120 random sample plots of 400 m2, we applied adaptive cluster sampling for trees with a diameter at breast height (DBH) of at least 6 cm. In addition, tree regeneration (DBH < 6 cm) was assessed.ResultsIn the core zone, F. hodginsii, A. spectabilis and Q. platycalyx occurred at moderate densities (4.9, 5.1 and 4.4 trees∙ha−1, respectively). F. hodginsii and A. spectabilis were however much less abundant in the buffer and restoration zones. In contrast, Q. platycalyx had its highest density in the restoration zone. Regeneration of all three target species occurred in the core zone; however, there were only a few regenerating trees of F. hodginsii and A. spectabilis in the buffer and regeneration zones. Regeneration of F. hodginsii and A. spectabilis was mostly in the vicinity of conspecific adult trees.ConclusionsF. hodginsii and A. spectabilis were mostly confined to the core zone, and regeneration of these species was rare in the buffer and restoration zones. For these two species, the core zone was the most important refuge, so continued conservation of this zone is important for the preservation of these species. The results of this study in the Ta Xua Nature Reserve do not confirm the classification of Q. platycalyx as ‘vulnerable’ in the Vietnam Red List. Further forest monitoring including repeated population assessments is needed to evaluate the vulnerability of threatened tree species.