Nonparametric and Semiparametric Estimation in Complex Surveys

Publisher Summary This chapter focuses on nonparametric and semi-parametric methods in two important statistical areas: estimation of densities and estimation of regression functions. Both of these areas have applications in survey estimation, for both descriptive and analytical uses. Orthogonal decomposition is a non-parametric regression method with good statistical properties that is applicable in situations where the mean function is not necessarily smooth. Neural networks are a class of methods conceptually related to penalized spline regression, in which the parameters are found by nonlinear regression. The semi-parametric model is particularly useful when some of the covariates in a data set are categorical, which by definition cannot be smoothed. In addition to nonparametric regression for multivariate data, another important extension is for models with more complex mean structures, including nonparametric equivalents of generalized linear models. Nonparametric regression applications require the specification of one or several smoothing parameters such as the bandwidth in kernel regression or the penalty in spline regression.