Yuefeng Han, Likai Chen, Wei Biao Wu
arXiv 23 Nov 2025 · Mathematics — Statistics Theory · publishedIEEE Transactions on Information Theory (2025)
arXiv:2511.18641 · PDF · DOI · OpenAlex · Extracted main text
High-dimensional vector autoregressive (VAR) models have numerous applications in fields such as econometrics, biology, climatology, among others. While prior research has mainly focused on linear VAR models, these approaches can be restrictive in practice. To address this, we introduce a high-dimensional non-parametric sparse additive model, providing a more flexible framework. Our method employs basis expansions to construct high-dimensional nonlinear VAR models. We derive convergence rates and model selection consistency for least squared estimators, considering dependence measures of the processes, error moment conditions, sparsity, and basis expansions. Our theory significantly extends prior linear VAR models by incorporating both non-Gaussianity and non-linearity. As a key contribution, we derive sharp Bernstein-type inequalities for tail probabilities in both non-sub-Gaussian linear and nonlinear VAR processes, which match the classical Bernstein inequality for independent random variables. Additionally, we present numerical experiments that support our theoretical findings and demonstrate the advantages of the nonlinear VAR model for a gene expression time series dataset.
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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 | Ravikumar, Pradeep and Lafferty, John and Liu, Han and Wasserman, La… (2009) Sparse additive models | 1.000 | 8 | 3 | 100% |
| 2 | Basu, Sumanta and Michailidis, George (2015) Regularized estimation in sparse high-dimensional time series models | 1.000 | 5 | 4 | 100% |
| 3 | Zhou, Hao Henry and Raskutti, Garvesh (2018) Non-parametric sparse additive auto-regressive network models | 0.811 | 4 | 2 | 100% |
| 4 | Hall, Eric C and Raskutti, Garvesh and Willett, Rebecca M (2018) Learning High-Dimensional Generalized Linear Autoregressive Models | 0.737 | 3 | 2 | 100% |
| 5 | Lim, Néhémy and d’Alché-Buc, Florence and Auliac, Cédric and Michail… (2015) Operator-valued kernel-based vector autoregressive models for network inference | 0.737 | 3 | 2 | 100% |
| 6 | Raskutti, Garvesh and Wainwright, Martin J and Yu, Bin (2012) Minimax-optimal rates for sparse additive models over kernel classes via convex programming | 0.737 | 3 | 2 | 100% |
| 7 | Pradeep Ravikumar and Martin J. Wainwright and John D. Lafferty (2010) High-dimensional Ising model selection using $ _1$-regularized logistic regression | 0.737 | 3 | 2 | 100% |
| 8 | Han, Fang and Lu, Huanran and Liu, Han (2015) A direct estimation of high dimensional stationary vector autoregressions | 0.644 | 2 | 2 | 100% |
| 9 | Merlevède, Florence and Peligrad, Magda and Rio, Emmanuel (2009) Bernstein inequality and moderate deviations under strong mixing conditions | 0.644 | 2 | 2 | 100% |
| 10 | Oliveira, Roberto Imbuzeiro (2016) The lower tail of random quadratic forms with applications to ordinary least squares | 0.644 | 2 | 2 | 100% |
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