Bias Adjustment for Mean Squared Error Estimation in M‐Quantile Models for Small Area Estimation

Summary M‐quantile (MQ) regression provides a robust and flexible alternative to mixed models for small area estimation. However, several theoretical aspects remain underexplored. In this paper, a parametric bootstrap method is proposed to approximate the distributions of area‐specific MQ coefficients and applied to adjust the bias in the mean squared error (MSE) estimation of predictors for population means. The unified bias adjustment method, based on the laws of total expectation and variance, is general and can be applied to any MSE estimator that neglects the uncertainty in predicting MQ coefficients. Simulation experiments evaluate the performance of the adjusted MSE estimators under different scenarios, including those with atypical values. A real‐world case study illustrates the practical relevance of the proposed methodology.