Muhammad Hanif

Generalized Multivariate Ratio and Regression Estimators: Generalized Univariate and Multivariate Ratio and Regression Estimators for Two-phase and ... Sampling Using Multi-auxiliary Variables Muhammad Hanif

The concept of two-phase sampling was first given by Neyman (1938), later on several simple and general regression and ratio estimators have been suggested, starting from Mohanty (1967), Srivastava (1970), Chand (1975), Kiregyera (1980, 84), Mukerjee et al. (1987), Srivastava et al.(1990), Roy (2003)and Samiuddin and Hanif (2006,07). Use of multi-auxiliary information for ratio and regression estimators, were considered, by Olkin (1958), Goswami and Sukhatme (1965), Raj (1965), Rao and Mudholkar (1967), Tripathi (1970, 1976), Tripathi and Ahmed (1995), Sen (1972), Tripathi (1987), Singh and Namjoshi (1988), Tripathi and Khattree (1989), Tripahi and Chaubey (1993), Ahmed (2003), Martin and Steven (2004) and Ahmad at el. (2008). In this monograph we have provided general classes of regression and ratio estimators for two-phase and multi-phase sampling using multi-auxiliary variables for estimating single as well as multiple variables of interest. The theoretical developments provided in this monograph can be useful in multipurpose surveys in which the problem is to estimate population means of several variables simultaneously in the field like agricultural, forestry etc.