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.

翻译：截断偏态正态分布的参数估计具有挑战性，因为截断会在似然函数中引入额外的非线性，并常常导致现有估计程序出现数值不稳定性。本文提出一种基于网格的估计方法（称为GRID-MOM），用于截断偏态正态分布的参数估计。该方法将形状参数固定在预先指定的网格上，并在每个网格点上使用矩估计法估计位置参数和尺度参数。随后通过基于似然的比较选择形状参数的最优值，从而得到最终的参数估计。通过将形状参数的估计与位置参数和尺度参数的估计解耦，所提方法降低了优化问题的复杂性并提高了数值稳定性。我们通过广泛的数值研究评估了所提估计量的有限样本性能，并在多种情境下将其与现有方法进行比较。结果表明，所提方法能够提供稳定且准确的估计，尤其对于形状参数，这表明该方法为截断偏态正态模型的推断提供了一种实用的替代方案。我们进一步利用磷酸化蛋白质组学数据和医院入院数据展示了所提方法的实际适用性。