On parameter estimation for the truncated skew-normal distribution

2026-03-06

AI Summary

This study addresses the challenging problem of parameter estimation for truncated skew-normal distributions, which is hindered by the high nonlinearity and numerical instability of the likelihood function. To overcome these difficulties, the authors propose the GRID-MOM method, which decouples the estimation of the shape parameter from those of location and scale by fixing the shape parameter on a pre-specified grid. This approach integrates method-of-moments estimation with likelihood-based model selection, substantially reducing optimization complexity and enhancing numerical stability. Extensive experiments across diverse simulation scenarios and real-world datasets—including phosphoproteomics data and hospital admission records—demonstrate that the proposed method achieves superior accuracy and robustness, particularly in estimating the shape parameter, compared to existing alternatives.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Parameter estimation for the truncated skew-normal distribution is challenging, as truncation introduces additional nonlinearity into the likelihood function and often leads to numerical instability in existing estimation procedures. In this paper, we propose a grid-based estimation method, referred to as GRID-MOM, for parameter estimation in the truncated skew-normal distribution. The proposed approach fixes the shape parameter on a pre-specified grid and, for each grid point, estimates the location and scale parameters using the method of moments. The optimal value of the shape parameter is then selected via likelihood-based comparison, yielding the final parameter estimates. By decoupling the estimation of the shape parameter from that of the location and scale parameters, the proposed method reduces the complexity of the optimization problem and improves numerical stability. We evaluate the finite-sample performance of the proposed estimator through an extensive numerical study, comparing it with existing methods under a variety of scenarios. The results demonstrate that the proposed method provides stable and accurate estimation, particularly for the shape parameter, suggesting that the proposed method offers a practical alternative for inference in truncated skew-normal models. We further demonstrate the practical applicability of the proposed method using phosphoproteomics data and hospital admission data.

Problem

• truncated skew-normal distribution
• parameter estimation
• numerical instability
• likelihood function
• shape parameter

Innovation

• truncated skew-normal distribution
• parameter estimation
• grid-based method
• method of moments
• numerical stability