Efficient Estimation of Nonlinear Finite Population Parameters Using Nonparametrics

Details Efficient Estimation of Nonlinear Finite Population Parameters Using Nonparametrics Efficient Estimation of Nonlinear Finite Population Parameters Using Nonparametrics

2012-01-06

arxiv.org/abs/1201.1375v1

Statistics

Methodology

Scientific paper

Nowadays, the high-precision estimation of nonlinear parameters such as quantiles, Gini indices or other measures of inequality is particularly crucial. In the present paper, we propose a general class of estimators for such parameters that take into account complete univariate auxiliary information. We construct unique survey weights through a nonparametric model-assisted approach that can be used by means of the plugg-in principle to estimate the nonlinear parameters. The asymptotic variance based on influence function linearization is derived and variance estimators are shown to be consistent under mild assumptions. Importantly, the gain in efficiency for the estimation of a nonlinear parameter depends on the prediction quality of the model for the linearized variable. Because linearized variables may be quite complex, linear models are unlikely to perform well and are outperformed by nonparametric models even if the study variable is linearly related with the auxiliary one. The theory is detailed for B-spline estimators including practical implementation and guidelines for choosing the smoothing parameters. A new calibration method is suggested and relationships with nonparametric model-calibration are explored. The applicability of the method is demonstrated on data extracted from the French Labour Force Survey and M\'ediam\'etrie television audience survey. Specifically, point and confidence intervals estimation of the Gini index are derived.

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