IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 13, Issue 1 Ver. III (Jan. - Feb. 2017), PP 59-63 www.iosrjournals.org DOI: 10.9790/5728-1301035963 www.iosrjournals.org 59 | Page A Generalised Class of Unbiased Seperate Regression Type Estimator under Stratified Random Sampling Shashi Bhushan 1 , Praveen Kumar Misra 1 1 Department of Mathematics and Statistics, Dr. Shakuntala Misra National Rehabilitation University, India Abstract: In this paper a generalized class of regression type estimators using the auxiliary information on population mean and population variance is proposed under stratified random sampling. In order to improve the performance of the proposed class of estimator, the Jack-knifed versions are also proposed. A comparative study of the proposed estimator is made with that of separate ratio estimator, separate product estimator, separate linear regression estimator and the usual stratified sample mean. It is shown that the estimators through proposed allocation always give more efficient estimators in the sense of having smaller mean square error than those obtained through Neyman Allocation. Keywords: Auxiliary information, ratio type Estimator, Bias, Mean Square Error. I. Introduction of the Proposed Estimator Let a population of size ‘N’ be stratified in to ‘L’ non-overlapping strata, the th h stratum size being h N (h=1,2,……,L) and 1 L h h N N    . Suppose ‘y’ be charectarstic under study and ‘x’ be the auxiliary variable. We denote by hj y : The observation on the th j unit of the population for the charectarstic ‘y’ under study ( 1, 2, ......., ) h j N  in the th h stratum (h =1,2,…..,L) hj x : The observation on the th j unit of the population for the auxiliary charectarstic ‘x’ under study ( 1, 2, ......., ) h j N  in the th h stratum (h = 1,2,….,L). 1 1 2 2 2 2 1 1 1 1 , , 1 1 ( ), ( ) ( 1) ( 1) h h h h N N h hj h hj j j h h N N yh hj h xh hj h h j h h Y y X x N N S y Y S x X N N                 2 2 2 2 1 1 1 1 1 ( ), ( ) 1 ( )( ) ( 1) h h h N N xh hj h yh hj h j j h h N xyh hj h hj h h xh hj j h x X y Y N N S x X y Y S S N                   where h  is the population correlation coefficient between ‘x’ and ‘y’ for the th h stratum ( 1, 2, ......., ) h j N  . 2 2 2 2 02 20 2 2 2 2 , , yh h h xh h h yh xh h h h h h S Y S R C C X Y Y X X        1 1 ( )( ): L p q pqh hj h hj h j h x X y Y N       the (,) th pq population product moment about mean between ‘x’ and ‘y’ for the th h stratum ( 1, 2, ......, ) h L  . 2 2 30 40 1 2 2 2 20 20 , h h h h h h         , 2 xyh yh h h xh xh S S S S     be the population regression coefficient of y on x for the th h stratum ( 1, 2, ......, ) h L  .