  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.
