Mean estimation based on the factor-type estimator under an adaptive cluster sampling design

If a sample is designated by a standard sampling strategy and if the character of the study satisfies a predetermined statement for an independent unit in the sample, then the items in the locality remain automatically in the sample. This type of method of selection of sampling units is called adaptive cluster sampling. This manuscript emphasizes the use of the factor-type estimator designed for population mean of the variable under study using the data of highly correlated auxiliary (supplementary) variable under adaptive cluster sampling. The bias, mean squared error and optimum mean squared errors up to the first order is obtained and a simulation study is performed for comparison purpose.