arXiv 13 Nov 2023 · Mathematics — Statistics Theory · 1 citations (OpenAlex)
arXiv:2311.07243 · PDF · DOI · OpenAlex · Extracted main text
This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified. A local principal component analysis method is proposed to estimate the factor structure and recover information on latent variables and latent functions, which combines $K$-nearest neighbors matching and principal component analysis. Large-sample properties are established, including a sharp bound on the matching discrepancy of nearest neighbors, sup-norm error bounds for estimated local factors and factor loadings, and the uniform convergence rate of the factor structure estimator. Under mild conditions our estimator of the latent factor structure can achieve the optimal rate of uniform convergence for nonparametric regression. The method is illustrated with a Monte Carlo experiment and an empirical application studying the effect of tax cuts on economic growth.
appendix boundary found by appendix_command · 67% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Zhang, Levina, and Zhu (2017) Estimating Network Edge Probabilities by Neighbourhood Smoothing | 1.000 | 5 | 3 | 100% |
| 2 | Zhang and Zha (2004) Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment | 0.928 | 4 | 3 | 100% |
| 3 | Abadie (2021) Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects | 0.644 | 2 | 2 | 100% |
| 4 | Feng (2023) Causal Inference in Possibly Nonlinear Factor Models self | 0.644 | 2 | 2 | 100% |
| 5 | Fernández-Val, Freeman, and Weidner (2021) Low-Rank Approximations of Nonseparable Panel Models | 0.644 | 2 | 2 | 100% |
| 6 | Stone (1982) Optimal Global Rates of Convergence for Nonparametric Regression | 0.644 | 2 | 2 | 100% |
| 7 | Abbe, Fan, Wang, and Zhong (2020) Entrywise Eigenvector Analysis of Random Matrices with Low Expected Rank | 0.481 | 6 | 2 | 17% |
| 8 | Ahn and Horenstein (2013) Eigenvalue Ratio Test for the Number of Factors | 0.405 | 1 | 1 | 100% |
| 9 | Arias-Castro, Lerman, and Zhang (2017) Spectral Clustering Based on Local PCA | 0.405 | 1 | 1 | 100% |
| 10 | Bai and Li (2014) Theory and Methods of Panel Data Models with Interactive Effects | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 28 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Flexible Imputation of Incomplete Network Data | 1.000 | 13 | 3 |
| 2 | Estimation of Panel Data Models with Nonlinear Factor Structure$^$ | 0.511 | 2 | 1 |
| 3 | Identification of Average Treatment Effects in Nonparametric Panel Models | 0.405 | 1 | 1 |
| 4 | Inferring Treatment Effects in Large Panels by Uncovering Latent Similarities | 0.405 | 1 | 1 |