Robust Parameter Estimation in PLMs with Skewed and Heavy-tailed Error Distributions

Partially linear models (PLMs) provide a flexible extension of classical linear models by incorporating parametric and nonparametric components, making them suitable for complex data structures often encountered in economics and biometrics. Traditionally, these models assume normally distributed errors, an assumption that may not hold in many practical scenarios. To address this, previous studies introduced the skew normal distribution in PLMs (PLM-SN) to account for asymmetry. However, such data sets may also exhibit heavy tails and skewness. To capture both characteristics, we propose a new approach: modeling the error structure using the skewed Laplace normal distribution (PLM-SLN), which maintains the same number of parameters as PLM-SN but better accommodates heavy-tailed behavior. An efficient estimation procedure using an expectation-conditional maximization (ECM) algorithm is developed to compute maximum likelihood estimates. The proposed method is validated using simulation experiments and applied to an empirical dataset to highlight its practical utility.