Prediction of Finite Population Total under Nonignorable Nonresponse Using Response and Nonresponse Distributions
Abdulhakeem A.H. Eideh
Department of Mathematics, Al-Quds University, Abu-Dies Campus, Palestine

This paper defined and studies the use of the response and nonresponse distributions for the prediction of finite population totals under single-stage sampling, when the sampling design is noninformative and missing value mechanism is nonignorable. The proposed predictors employ the response set values of the target study variable, the weights of the response set units. The prediction problem is treated by estimating the expectations of the study values for unobserved units in sample – nonresponse set, and for non-sample units. We apply the proposed new method, under three population models, namely: common mean population model, simple ratio population model, and simple regression population model. The main features of the present predictors are their behaviours in terms of the nonignorable nonresponse parameters. Also the use of the best linear unbiased predictors and estimators that ignore the nonignorable nonresponse yield biased predictors and bias estimators.Furthermore, we introduce new test for the testing ignorability of nonresponse based on the Kullback-Leibler information measure.

Bethlehem, J.G. (1988). Reduction of nonresponse bias through regression estimation. Journal of Official Statistics, 4, pp 251-260.

Eideh A.H. (2009). On the use of the sample distribution and sample likelihood for inference under informative probability sampling. DIRASAT (Natural Science), Volume 36 (2009), Number 1, pp18-29.

Eideh, A. H. and Nathan, G. (2009). Two-stage informative cluster sampling with application in small area estimation. Journal of Statistical Planning and Inference.139, pp 3088-3101.

Sverchkov, M., and Pfeffermann, D. (2004). Prediction of finite population totals based on the sample distribution. Survey Methodology, 30, pp 79-92.

Keywords: Probability-Weighted Estimator; Nonignorable Nonresponse; Response distribution.; Kullback-Leibler Information Measure

Biography: Abdulhakeem Eideh, Al-Quds University, Palestine, is sampling: designa and analysis consultants, academic, and trainer for official statistics, in particular, Palestinian Central Bureau of Statistics. Since 2001, Abdulhakeem vists Univ of Southampton (S3RI) 10 times. Most of Abdulhakeem career is an academic statistician with resposibilities for teaching and research: analysis of complex survey data. Abdulhakeem married with Hudda and has a family with six children: