  In many applications, linear models fit the data poorly. This article studies
an appealing alternative, the generalized regression model. This model only
assumes that there exists an unknown monotonically increasing link function
connecting the response $Y$ to a single index $X^T\beta^*$ of explanatory
variables $X\in\mathbb{R}^d$. The generalized regression model is flexible and
covers many widely used statistical models. It fits the data generating
mechanisms well in many real problems, which makes it useful in a variety of
applications where regression models are regularly employed. In low dimensions,
rank-based M-estimators are recommended to deal with the generalized regression
model, giving root-$n$ consistent estimators of $\beta^*$. Applications of
these estimators to high dimensional data, however, are questionable. This
article studies, both theoretically and practically, a simple yet powerful
smoothing approach to handle the high dimensional generalized regression model.
Theoretically, a family of smoothing functions is provided, and the amount of
smoothing necessary for efficient inference is carefully calculated.
Practically, our study is motivated by an important and challenging scientific
problem: decoding gene regulation by predicting transcription factors that bind
to cis-regulatory elements. Applying our proposed method to this problem shows
substantial improvement over the state-of-the-art alternative in real data.
