Regression method has been widely used to explore relationship between dependent and independent variables. In practice, data issues such as censoring and missing data often exist. When the response variable is (fixed) censored, Tobit regression models have been widely employed to explore the relationship between the response variable and covariates. In this paper, we extend conventional parametric Tobit models to a novel semi-parametric regression model by replacing the linear components in Tobit models with nonparametric additive components, which we refer as Tobit additive models, and propose a likelihood based estimation method for Tobit additive models. %The proposed estimation method is computational efficient and easy to implement. Numerical experiments are conducted to evaluate the finite sample performance. The estimation method works well in finite sample experiments, even when sample size is relative small.

翻译：回归法被广泛用于探讨依附性和独立变量之间的关系。在实践中,审查和缺失数据等数据问题往往存在。当响应变量受到(固定)审查时, Tobit 回归模型被广泛用于探讨响应变量和共变之间的关系。在本文中,我们将传统的参数Tobit 模型推广到一个新的半参数回归模型,将Tobit 模型中的线性成分替换为非参数添加成分,我们称之为Tobit 添加模型,并提出了 Tobit 添加模型的基于可能性的估计方法。%提议的估算方法具有计算效率,易于实施。进行了定量实验,以评价有限的样本性能。在有限的样本实验中,即使样本规模相对小,估算方法也很有效。