Gaussian Transforms Modeling and the Estimation of Distributional Regression Functions
提出条件累积分布函数的灵活高斯表示，并给出凹似然准则进行估计，统一了条件密度、分布和分位数的最大似然估计框架，在美国性别工资差距数据中展示了应用。
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative distribution functions, including in finite samples and under general misspecification. We use these representations to provide a unified framework for the flexible maximum likelihood estimation of conditional density, cumulative distribution, and quantile functions at parametric rate. Our formulation yields substantial simplifications and finite sample improvements over related methods. An empirical application to the gender wage gap in the United States illustrates our framework.