A Study On Some Theories In Calibration Approach

Calibration approach has developed vastly into an important field of research in survey sampling. It is a methodology under which weights are computed incorporating auxiliary information in such a way that the resulting estimator is randomization consistent.This paper studies the use of calibration approach to estimate population parameter at the estimate stage under the uniform framework of modern sampling theory.This study starts with a description of the Generalised Regression (GREG) approach and basic calibration approach—Minimization Measurement Method. These two approaches are alternative but conceptually different ways to use auxiliary information. GREG estimator translates into a calibration estimator in linear form, so the design and model based properties of it could be used to calibration estimation. Then we get the instrumental vector method (also named generalized calibration) by replacing the distance minimization argument with a function that incorporates an instrumental vector. GREG approach shows to be a special case of instrumental vector method as z=x. The general conclusions we get in Chapter 3 propose a deep theoretical foundation for the following chapters.In Chapter 4, calibration is used in a range of different survey settings with complex auxiliary information (information made up for several components). We examine several situations, including stratified sampling, two-phases sampling and two-stage sampling. In Chapter 5, Generalizations to more complex parameters are then considered, including population quantiles, distribution function and variance. Variances of the resulting estimators are not presentable in simple form. Close approximation is possible via the corresponding linearized statistic. We also put light on how calibration weighting ideas can be used to compensate for non-response error.In Chapter 6, we view calibration as an algebraic problem, and the calibrated weights as the solution of a "convex mathematical programming problem". We set up a matrix formulation of the calibration problem, and use the mathematical approach, building on matrix theory and mathematical programming, determining a boundary for the weights. We further deal with the existence and uniqueness of the solution to the programming problem. Necessary conditions for the existence of weights that satisfy the calibration equation are also given. The computational aspects of calibration are also discussed.Simulation studies have been conducted in every chapter to test the performance of proposed estimators.