Two stage inverse adaptive cluster sampling with stopping rule depends upon the size of cluster. (English) Zbl 1442.62029
Consider a finite population of size \(N\) divided into \(K\) non-overlapping clusters each of size \(N_i\), \(i=1,2,\dots,K\). In the first stage, a probability proportional to size sample of size \(k\) without replacement (ppswor) is selected. At the second stage, a simple random sample of size \(n_i\) \((i=1,2,\dots,k)\) is drawn without replacement from the \(i\)th cluster adding up to \(n\) initial sampling units. For each of the selected units, a prespecified condition \(C\) is verified and if at least \(r_i\) units, \(i=1,2,\dots,k\) of the \(n_i\) satisfy \(C\), then sampling is stopped. If not, it is continued until either \(r_i\) units are selected or a prefixed total number of units are selected from the \(i\)th cluster. If \(C\) is satisfied for a unit in the \(i\)th cluster, Thompson’s Adaptive network is formed.
This procedure gives a new design which is a combination of inverse adaptive cluster sampling and two-stage cluster sampling. Estimation procedure is suggested for the above design. The ordered estimates thus obtained are improved upon by unordering using Rao-Blackwellization. This new design is applied to the problem of estimating the total number of thorny plants in an area of 400 acres in the Tamhini (Western) Ghats of India, a large number of which is unsafe for evergreen plants. Monte Carlo simulation study is presented towards the end of the paper to compare with conventional inverse adaptive sampling and two stage cluster sampling.
This procedure gives a new design which is a combination of inverse adaptive cluster sampling and two-stage cluster sampling. Estimation procedure is suggested for the above design. The ordered estimates thus obtained are improved upon by unordering using Rao-Blackwellization. This new design is applied to the problem of estimating the total number of thorny plants in an area of 400 acres in the Tamhini (Western) Ghats of India, a large number of which is unsafe for evergreen plants. Monte Carlo simulation study is presented towards the end of the paper to compare with conventional inverse adaptive sampling and two stage cluster sampling.
Reviewer: T. J. Rao (Visakhapatnam)
MSC:
| 62D05 | Sampling theory, sample surveys |
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 62K10 | Statistical block designs |
| 62P12 | Applications of statistics to environmental and related topics |
Keywords:
adaptive cluster sampling (ACS); two stage sampling; general inverse adaptive sampling; Rao-Blackwellization; designReferences:
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