Nonparametric Model Calibration Estimation in Survey Sampling

• Published in: Journal of the American Statistical Association Vol. 100; no. 472; pp. 1429 - 1442
• Main Authors: Montanari, Giorgio E, Ranalli, M. Giovanna
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.12.2005; American Statistical Association; Taylor & Francis Ltd
• Subjects: Applications; Approximation; Auxiliary information; Calibration; Data collection; Distribution; Estimation; Estimation methods; Estimators; Exact sciences and technology; General topics; Generalized regression estimator; Geometry; Information; Linear regression; Local polynomials; Mathematical methods; Mathematics; Model-assisted approach; Neural networks; Nonparametric inference; Nonparametric models; Nonparametric regression; Parameter estimation; Polynomials; Population; Population estimates; Population mean; Probability and statistics; Regression analysis; Sampling; Sampling techniques; Sciences and techniques of general use; Statistical methods; Statistical models; Statistical variance; Statistics; Surveying; Theory and Methods; Variables; Polynomial; Parameter estimation; Sample size; Variance estimation; Non parametric method; Non parametric estimation; Superpopulation model; Statistical simulation; Superpopulation; Local polynomials; Variance; Learning; Model matching; Consistent estimator; Model-assisted approach; Distribution function; Stream; Sampling; Sample survey; Smoothing methods; Statistical moment; Nonparametric regression; Linear relation; Neural network; Mean value; Auxiliary information; Mean estimation; Functional; Statistical method; Smoothing; Experimental design; Neural networks; Generalized regression estimator; Asymptotic approximation; Application
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214505000000141

Calibration is commonly used in survey sampling to include auxiliary information at the estimation stage of a population parameter. Calibrating the observation weights on population means (totals) of a set of auxiliary variables implies building weights that when applied to the auxiliaries give exactly their population mean (total). Implicitly, calibration techniques rely on a linear relation between the survey variable and the auxiliary variables. However, when auxiliary information is available for all units in the population, more complex modeling can be handled by means of model calibration; auxiliary variables are used to obtain fitted values of the survey variable for all units in the population, and estimation weights are sought to satisfy calibration constraints on the fitted values population mean, rather than on the auxiliary variables one. In this work we extend model calibration considering more general superpopulation models and use nonparametric methods to obtain the fitted values on which to calibrate. More precisely, we adopt neural network learning and local polynomial smoothing to estimate the functional relationship between the survey variable and the auxiliary variables. Under suitable regularity conditions, the proposed estimators are proven to be design consistent. The moments of the asymptotic distribution are also derived, and a consistent estimator of the variance of each distribution is then proposed. The performance of the proposed estimators for finite-size samples is investigated by means of simulation studies. An application to the assessment of the ecological conditions of streams in the mid-Atlantic highlands in the United States is also carried out.