Temporal M-quantile models and robust bias-corrected small area predictors

TL;DR

This paper extends M-quantile models for small area estimation to handle time-dependent data robustly, addressing limitations of linear mixed models and providing bias-corrected predictors and MSE estimation.

Contribution

It introduces a novel robust M-quantile modeling approach for small area prediction with time series data, including bias correction and optimal robustness parameter selection.

Findings

Robust bias-corrected predictors outperform traditional methods.

Simulation studies validate the effectiveness of the proposed models.

Application to Spanish survey data demonstrates practical utility.

Abstract

In small area estimation, it is a smart strategy to rely on data measured over time. However, linear mixed models struggle to properly capture time dependencies when the number of lags is large. Given the lack of published studies addressing robust prediction in small areas using time-dependent data, this research seeks to extend M-quantile models to this field. Indeed, our methodology successfully addresses this challenge and offers flexibility to the widely imposed assumption of unit-level independence. Under the new model, robust bias-corrected predictors for small area linear indicators are derived. Additionally, the optimal selection of the robustness parameter for bias correction is explored, contributing theoretically to the field and enhancing outlier detection. For the estimation of the mean squared error (MSE), a first-order approximation and analytical estimators are obtained under general conditions. Several simulation experiments are conducted to evaluate the performance of the fitting algorithm, the new predictors, and the resulting MSE estimators, as well as the optimal selection of the robustness parameter. Finally, an application to the Spanish Living Conditions Survey data illustrates the usefulness of the proposed predictors.