Murthy’s Estimator in Unequal Probability Inverse Adaptive Cluster Sampling

Sangngam, Prayad

doi:10.5539/mas.v6n11p20

Cited by 5 publications

(4 citation statements)

References 7 publications

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“…, we also recommend the unbiased estimator. For future studies, we can consider applying the ratio estimator in adaptive sampling schemes as suggested by Thompson (1990) and Sangngam (2013) for.…”

Section: Discussionmentioning

confidence: 99%

Ratio Estimators Using Coefficient of Variation and Coefficient of Correlation

Sangngam¹

2014

MAS

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This paper introduces ratio estimators of the population mean using the coefficient of variation of study variable and auxiliary variables together with the coefficient of correlation between the study and auxiliary variables under simple random sampling and stratified random sampling. These ratio estimators are almost unbiased. The mean square errors of the estimators and their estimators are given. Sample size estimation in both sampling designs are presented. An optimal sample size allocation in stratified random sampling is also suggested. Based on theoretical study, it can be shown that these ratio estimators have smaller MSE than the unbiased estimators. Moreover, the empirical study indicates that these ratio estimators have smallest MSE compared to the existing ones.

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Section: Discussionmentioning

confidence: 99%

Ratio Estimators Using Coefficient of Variation and Coefficient of Correlation

Sangngam¹

2014

MAS

Self Cite

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“…Sangngam () introduced an unbiased estimator of τ for use in an unequal probability inverse sampling design given by

{\overset{τ}{true}}_{S} = N false(\overset{p}{true} {\bar{y}}_{c} + (1 - \overset{false^}{p}) {\bar{y}}_{\bar{c}} false),

where

\overset{false^}{p} = false(m - 1 false) / false(n_{0} - 1 false)

{\overset{y}{true}}_{c} = \frac{1}{m} \sum_{i \in S_{c}} y_{i}^{*} / p_{i}^{*}

and

{\overset{y}{true}}_{\overset{c}{true}} = \frac{1}{n_{0} - m} \sum_{i \in S_{\overset{c}{true}}} y_{i}^{*} / p_{i}^{*} .

The quantities

y_{i}^{*}

and

p_{i}^{*}

are the sum of the y and selection probability values of units belonging to network i , respectively. The number of units selected sequentially which are required to obtain m rare units before adding neighbouring units is

n_{s}

.…”

Section: Estimatorsmentioning

confidence: 99%

“…Inverse sampling with unequal selection probabilities (and with replacement) was introduced by Greco & Naddeo (). Sangngam () introduced an unbiased estimator for use with unequal probability inverse sampling designs, where initial units are selected with replacement. In such sampling designs, the number of distinct rare units may be smaller than the predetermined number of rare units because sampling is with replacement.…”

Section: Introductionmentioning

confidence: 99%

Inverse Adaptive Cluster Sampling with Unequal Selection Probabilities: Case Studies on Crab Holes and Arsenic Pollution

Salehi

Moradi

Al‐Khayat

et al. 2015

Aus NZ J of Statistics

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SummaryAdaptive cluster sampling is an efficient method of estimating the parameters of rare and clustered populations. The method mimics how biologists would like to collect data in the field by targeting survey effort to localised areas where the rare population occurs. Another popular sampling design is inverse sampling. Inverse sampling was developed so as to be able to obtain a sample of rare events having a predetermined size. Ideally, in inverse sampling, the resultant sample set will be sufficiently large to ensure reliable estimation of population parameters. In an effort to combine the good properties of these two designs, adaptive cluster sampling and inverse sampling, we introduce inverse adaptive cluster sampling with unequal selection probabilities. We develop an unbiased estimator of the population total that is applicable to data obtained from such designs. We also develop numerical approximations to this estimator. The efficiency of the estimators that we introduce is investigated through simulation studies based on two real populations: crabs in Al Khor, Qatar and arsenic pollution in Kurdistan, Iran. The simulation results show that our estimators are efficient.

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“…They believed that the method could be applied at a national level. Also, Sangngam () incorporated unequal probability inverse sampling with adaptive cluster sampling where the probabilities were computed based on an auxiliary variable. He evaluated his design using the ring‐necked duck data (Smith, Conroy, & Brakhage, ) and showed the proposed strategy was efficient with a highly correlated auxiliary variable.…”

Section: Introductionmentioning

confidence: 99%

Group inverse sampling: An economical approach to inverse sampling

Panahbehagh

Smith

2017

Environmetrics

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Inverse sampling is an adaptive design in the sense that the final sampling effort during a search for rare events will depend on what is found during the survey. Conventional inverse sampling (CIS) designs successively select individual sampling units to find, for example, the kth rare event. In real sampling situations, use of successive one‐by‐one sampling can be cost prohibitive. Here, we introduce an inverse sampling design that uses successive selection of groups instead of individuals, named group inverse sampling (GIS). An unbiased estimator and its variance estimator of the population mean are derived based on the Murthy estimator. CIS is a special case of the generalized design with group size equal to one. We simulate the GIS design to evaluate its efficiency using populations of rare freshwater mussels in West Virginia, USA. For cost consideration, we calculate distance traveled among the sampling units. Results show that GIS was more cost efficient than CIS in all cases. The group size for successive sampling (d) was the most influential design parameter for reducing cost and increasing precision. Also, GIS found more rare units with greater consistency compared to simple random sampling without replacement (SRS). An important characteristic of the GIS design is that sampling stops when the target number of rare units is found, which prevents unnecessary sampling and contrasts favorably with other adaptive designs such as adaptive cluster sampling.

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Murthy’s Estimator in Unequal Probability Inverse Adaptive Cluster Sampling

Cited by 5 publications

References 7 publications

Ratio Estimators Using Coefficient of Variation and Coefficient of Correlation

Ratio Estimators Using Coefficient of Variation and Coefficient of Correlation

Inverse Adaptive Cluster Sampling with Unequal Selection Probabilities: Case Studies on Crab Holes and Arsenic Pollution

Group inverse sampling: An economical approach to inverse sampling

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