Generalized robust regression techniques and adaptive cluster sampling for efficient estimation of population mean in case of rare and clustered populations.

Situations when field researchers are tempted to deviate from preselected sampling plan and to include nearby or related units in sample, then adaptive cluster sampling (ACS) offers a nearly completion solution. For rare and clustered populations, Thompson introduced ACS as an effective sampling method when data is not contaminated with outliers. However, traditional approaches produce distorted results when data includes outliers. Taking the same issue into consideration, the present study focuses on defining adaptive ratio-type regression estimators using OLS, Huber M, Mallows GM, Schweppe GM, SIS GM and Uk's redescending M-estimation functions within ACS framework. Subsequently, we propose regression type estimators utilizing these functions within ACS framework. In this study, we have also derived mean square error properties of both adapted and proposed estimators in order to evaluate performance of these estimators, by using both real-life data and simulated data sets generated from a Poisson clustered process.