# A Likelihood Ratio Framework for High Dimensional Semiparametric Regression

arXiv: https://arxiv.org/abs/1412.2295 · HTML: https://mlsanity.com/paper/1412.2295/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2014.

## Built on by (most cited first, 3 of 3)

- [A Computationally Efficient Method for Learning Exponential Family Distributions](https://mlsanity.com/paper/2110.15397/) (2021)
- [On Computationally Efficient Learning of Exponential Family Distributions](https://mlsanity.com/paper/2309.06413/) (2023)
- [Computational Efficient and Minimax Optimal Nonignorable Matrix Completion](https://mlsanity.com/paper/2504.04016/) (2025)

## Abstract (arXiv)

We propose a likelihood ratio based inferential framework for high dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high dimensional data analysis, including incomplete data, selection bias, and heterogeneous multitask learning. Our work has three main contributions. (i) We develop a regularized statistical chromatography approach to infer the parameter of interest under the proposed semiparametric generalized linear model without the need of estimating the unknown base measure function. (ii) We propose a new framework to construct post-regularization confidence regions and tests for the low dimensional components of high dimensional parameters. Unlike existing post-regularization inferential methods, our approach is based on a novel directional likelihood. In particular, the framework naturally handles generic regularized estimators with nonconvex penalty functions and it can be used to infer least false parameters under misspecified models. (iii) We develop new concentration inequalities and normal approximation results for U-statistics with unbounded kernels, which are of independent interest. We demonstrate the consequences of the general theory by using an example of missing data problem. Extensive simulation studies and real data analysis are provided to illustrate our proposed approach.