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.

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 variablewhich is highly negatively correlatedwith 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(JAmStat 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.

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 k-step ACS based on Horvitz-Thompson （HT） estimator was developed and an unbiased estimator was derived. The k-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 k-step ACS-HT estimator. The effectiveness of using different k- step sizes was also compared. The results showed that k-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, k-step ACS without replacement was slightly more effective than that with replacement. In k-step ACS, the variance estimate of one-step ACS is much larger than other k-step ACS （k 〉 1）, but it is smaller than ACS. This implies that k-step ACS is more effective than traditional ACS, besides, the final sample size can be controlled easily in population with big clusters.