The Annals of Applied Statistics

Prediction of small area quantiles for the conservation effects assessment project using a mixed effects quantile regression model

Emily Berg and Danhyang Lee

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Quantiles of the distributions of several measures of erosion are important parameters in the Conservation Effects Assessment Project, a survey intended to quantify soil and nutrient loss on crop fields. Because sample sizes for domains of interest are too small to support reliable direct estimators, model based methods are needed. Quantile regression is appealing for CEAP because finding a single family of parametric models that adequately describes the distributions of all variables is difficult and small area quantiles are parameters of interest. We construct empirical Bayes predictors and bootstrap mean squared error estimators based on the linearly interpolated generalized Pareto distribution (LIGPD). We apply the procedures to predict county-level quantiles for four types of erosion in Wisconsin and validate the procedures through simulation.

Article information

Ann. Appl. Stat., Volume 13, Number 4 (2019), 2158-2188.

Received: November 2017
Revised: April 2019
First available in Project Euclid: 28 November 2019

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Quantile regression empirical Bayes parametric bootstrap erosion environmental monitoring


Berg, Emily; Lee, Danhyang. Prediction of small area quantiles for the conservation effects assessment project using a mixed effects quantile regression model. Ann. Appl. Stat. 13 (2019), no. 4, 2158--2188. doi:10.1214/19-AOAS1276.

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Supplemental materials

  • Supplement to “Small area estimation for the conservation effects assessment project using a mixed effects quantile regression model”. We provide the link to the Github repository with code, the covariance matrix used for the initial estimators, a comparison to an iterative procedure similar to a full EM algorithm, a description of the mixed effects gamma model applied to the data, and versions of Figure 5 for Runoff, RUSLE2 and CDiff.