The sample selection bias problem occurs when the outcome of interest is only observed according to some selection rule, where there is a dependence structure between the outcome and the selection rule. In a pioneering work, J. Heckman proposed a sample selection model based on a bivariate normal distribution for dealing with this problem. Due to the non-robustness of the normal distribution, many alternatives have been introduced in the literature by assuming extensions of the normal distribution like the Student-t and skew-normal models. One common limitation of the existent sample selection models is that they require a transformation of the outcome of interest, which is common ${\mathbb{R}}^{+}$-valued, such as income and wage. With this, data are analyzed on a non-original scale which complicates the interpretation of the parameters. In this paper, we propose a sample selection model based on the bivariate Birnbaum–Saunders distribution, which has the same number of parameters that the classical Heckman model. Further, our associated outcome equation is ${\mathbb{R}}^{+}$-valued. We discuss estimation by maximum likelihood and present some Monte Carlo simulation studies. An empirical application to the ambulatory expenditures data from the 2001 Medical Expenditure Panel Survey is presented.

当仅根据某些选择规则观察感兴趣的结果时，就会出现样本选择偏差问题，其中结果与选择规则之间存在依赖结构。在一项开创性的工作中，J. Heckman 提出了一种基于二元正态分布的样本选择模型来处理这个问题。由于正态分布的非鲁棒性，文献中通过假设正态分布的扩展引入了许多替代方案，如 Student-t 和 skew-normal 模型。现有样本选择模型的一个常见限制是它们需要转换感兴趣的结果，这很常见${\mathbb{R}}^{+}$- 价值，例如收入和工资。这样，数据在非原始尺度上进行分析，这使参数的解释变得复杂。在本文中，我们提出了一个基于双变量 Birnbaum-Saunders 分布的样本选择模型，该模型与经典的 Heckman 模型具有相同数量的参数。此外，我们相关的结果方程是${\mathbb{R}}^{+}$-值。我们讨论最大似然估计并提出一些蒙特卡罗模拟研究。对 2001 年医疗支出小组调查中的门诊支出数据进行了实证应用。