# A Unified Framework for Estimation of High-dimensional Conditional Factor Models

arXiv: https://arxiv.org/abs/2209.00391 · HTML: https://mlsanity.com/paper/2209.00391/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 58 references that are in the map.
- First posted on arXiv 1 Sep 2022.

## Builds on (most cited first, 7 of 7)

- [Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview](https://mlsanity.com/paper/1809.09573/) (2018)
- [Inference and Uncertainty Quantification for Noisy Matrix Completion](https://mlsanity.com/paper/1906.04159/) (2019)
- [Statistical Inferences of Linear Forms for Noisy Matrix Completion](https://mlsanity.com/paper/1909.00116/) (2019)
- [Generalized High-Dimensional Trace Regression via Nuclear Norm Regularization](https://mlsanity.com/paper/1710.08083/) (2017)
- [Inference for Low-Rank Models](https://mlsanity.com/paper/2107.02602/) (2021)
- [Projected principal component analysis in factor models](https://mlsanity.com/paper/1406.3836/) (2014)
- [Nuclear Norm Regularized Estimation of Panel Regression Models](https://mlsanity.com/paper/1810.10987/) (2018)

## Abstract (arXiv)

This paper presents a general framework for estimating high-dimensional conditional latent factor models via constrained nuclear norm regularization. We establish large sample properties of the estimators and provide efficient algorithms for their computation. To improve practical applicability, we propose a cross-validation procedure for selecting the regularization parameter. Our framework unifies the estimation of various conditional factor models, enabling the derivation of new asymptotic results while addressing limitations of existing methods, which are often model-specific or restrictive. Empirical analyses of the cross section of individual US stock returns suggest that imposing homogeneity improves the model's out-of-sample predictability, with our new method outperforming existing alternatives.