Small area prediction of quantiles for zero-inflated data and an informative sample design

Abstract

The Conservation Effects Assessment Project (CEAP) is a survey intended to quantify soil and nutrient loss on cropland. Estimates of the quantiles of CEAP response variables are published. Previous work develops a procedure for predicting small area quantiles based on a mixed effects quantile regression model. The conditional density function of the response given covariates and area random effects is approximated with the linearly interpolated generalised Pareto distribution (LIGPD). Empirical Bayes is used for prediction and a parametric bootstrap procedure is developed for mean squared error estimation. In this work, we develop two extensions of the LIGPD-based small area quantile prediction procedure. One extension allows for zero-inflated data. The second extension accounts for an informative sample design. We apply the procedures to predict quantiles of the distribution of percolation (a CEAP response variable) in Kansas counties.

Keywords

• quantile regression
• mixed effects models
• bootstrap