Penalization and data reduction of auxiliary variables in survey sampling

Abstract : Survey sampling techniques are quite useful in a way to estimate population parameterssuch as the population total when the large dimensional auxiliary data setis available. This thesis deals with the estimation of population total in presenceof ill-conditioned large data set.In the first chapter, we give some basic definitions that will be used in thelater chapters. The Horvitz-Thompson estimator is defined as an estimator whichdoes not use auxiliary variables. Along with, calibration technique is defined toincorporate the auxiliary variables for sake of improvement in the estimation ofpopulation totals for a fixed sample size.The second chapter is a part of a review article about ridge regression estimationas a remedy for the multicollinearity. We give a detailed review ofthe model-based, design-based and model-assisted scenarios for ridge estimation.These estimates give improved results in terms of MSE compared to the leastsquared estimates. Penalized calibration is also defined under survey sampling asan equivalent estimation technique to the ridge regression in the classical statisticscase. Simulation results confirm the improved estimation compared to theHorvitz-Thompson estimator.Another solution to the ill-conditioned large auxiliary data is given in terms ofprincipal components analysis in chapter three. Principal component regression isdefined and its use in survey sampling is explored. Some new types of principalcomponent calibration techniques are proposed such as calibration on the secondmoment of principal component variables, partial principal component calibrationand estimated principal component calibration to estimate a population total. Applicationof these techniques on real data advocates the use of these data reductiontechniques for the improved estimation of population totals
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Muhammad Ahmed Shehzad. Penalization and data reduction of auxiliary variables in survey sampling. General Mathematics [math.GM]. Université de Bourgogne, 2012. English. ⟨NNT : 2012DIJOS010⟩. ⟨tel-00812880⟩

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