arXiv 21 Jun 2026 · Econometrics
arXiv:2606.22555 · PDF · DOI · OpenAlex · Extracted main text
We develop a framework for learning dependence structures from empirical dependence operators. Rather than treating cluster, factor, and sparse dependence as maintained assumptions, we represent them as covariance geometries in a common Hilbert space and summarize dependence through a low-dimensional dependence profile based on projection similarity scores. We establish identification under a principal-angle separation condition, prove consistency and asymptotic normality of the estimated profile, and derive finite-sample classification error bounds. We further show that when covariance-geometry tangent spaces overlap, no statistical procedure can distinguish the geometries at first order, providing a formal characterization of ambiguous dependence structures. Projection-residual diagnostics assess absolute goodness-of-fit and detect misspecified covariance dictionaries. Finally, we establish oracle adaptivity of profile-guided inference: dependence profiles can be used to select dependence-robust procedures in a data-driven manner, yielding inference that is asymptotically equivalent to an infeasible oracle that knows the dominant covariance geometry in advance.
appendix boundary found by appendix_command · 43% 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 | Hansen, Bruce E (2007) Least Squares Model Averaging | 0.843 | 3 | 3 | 100% |
| 2 | Auerbach, Eric (2019) Identification and Estimation of a Partially Linear Regression Model Using Network Data | 0.644 | 3 | 2 | 67% |
| 3 | Bai, Jushan (2003) Inferential Theory for Factor Models of Large Dimensions | 0.644 | 3 | 2 | 67% |
| 4 | Bai, Jushan and Ng, Serena (2002) Determining the Number of Factors in Approximate Factor Models | 0.644 | 3 | 2 | 67% |
| 5 | Conley, Timothy G (1999) GMM Estimation with Cross Sectional Dependence | 0.644 | 3 | 2 | 67% |
| 6 | Leung, Michael P (2022) Causal Inference Under Approximate Neighborhood Interference | 0.644 | 3 | 2 | 67% |
| 7 | Bates, J. M. and Granger, C. W. J (1969) The Combination of Forecasts | 0.644 | 2 | 2 | 100% |
| 8 | Arellano, Manuel (1987) Computing Robust Standard Errors for Within-Groups Estimators | 0.511 | 2 | 1 | 100% |
| 9 | Bickel, Peter J. and Klaassen, Chris A. J. and Ritov, Ya'acov and We… (1993) Efficient and Adaptive Estimation for Semiparametric Models | 0.511 | 2 | 1 | 100% |
| 10 | Bickel, Peter J. and Levina, Elizaveta (2008) Covariance Regularization by Thresholding | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 33 scored citations.