  Currently, the high-precision estimation of nonlinear parameters such as Gini
indices, low-income proportions 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 univariate auxiliary information assumed
to be known for every unit in the population. Through a nonparametric
model-assisted approach, we construct a unique system of survey weights that
can be used to estimate any nonlinear parameter associated with any study
variable of the survey, using a plug-in principle. Based on a rigorous
functional approach and a linearization principle, the asymptotic variance of
the proposed estimators is derived, and variance estimators are shown to be
consistent under mild assumptions. The theory is fully detailed for penalized
B-spline estimators together with suggestions for practical implementation and
guidelines for choosing the smoothing parameters. The validity of the method is
demonstrated on data extracted from the French Labor Force Survey. Point and
confidence intervals estimation for the Gini index and the low-income
proportion are derived. Theoretical and empirical results highlight our
interest in using a nonparametric approach versus a parametric one when
estimating nonlinear parameters in the presence of auxiliary information.
