Chaohua Dong, Jiti Gao, Bin Peng, Yayi Yan
arXiv 5 Nov 2023 · Econometrics
arXiv:2311.02789 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we consider estimation and inference for the unknown parameters and function involved in a class of generalized hierarchical models. Such models are of great interest in the literature of neural networks (such as Bauer and Kohler, 2019). We propose a rectified linear unit (ReLU) based deep neural network (DNN) approach, and contribute to the design of DNN by i) providing more transparency for practical implementation, ii) defining different types of sparsity, iii) showing the differentiability, iv) pointing out the set of effective parameters, and v) offering a new variant of rectified linear activation function (ReLU), etc. Asymptotic properties are established accordingly, and a feasible procedure for the purpose of inference is also proposed. We conduct extensive numerical studies to examine the finite-sample performance of the estimation methods, and we also evaluate the empirical relevance and applicability of the proposed models and estimation methods to real data.
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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 | Bauer \ Kohler (2019) `On Deep Learning as a Remedy for the Curse of Dimensionality in Nonparametric Regression', The Annals of Statistics 47(4), 2261… | 0.965 | 10 | 4 | 90% |
| 2 | Farrell, Liang \ Misra (2021) `Deep neural networks for estimation and inference', Econometrica 89(1), 181–213 | 0.843 | 4 | 3 | 75% |
| 3 | Dubey, Singh \ Chaudhuri (2022) `Activation functions in deep learning: A comprehensive survey and benchmark', Neurocomputing 503, 92–108 | 0.737 | 3 | 3 | 67% |
| 4 | Fan \ Yao (2003) Nonlinear Time Series: Nonparametric and Parametric Methods, Springer-Verlag | 0.644 | 4 | 2 | 50% |
| 5 | Borup, Eriksen, Kjr \ Thyrsgaard (2023) `Predicting bond return predictability', Management Science, forthcoming | 0.644 | 4 | 1 | 100% |
| 6 | Du, Fan, Lv, Sun \ Vossler (2021) Dimension-free average treatment effect inference with deep neural networks | 0.644 | 2 | 2 | 100% |
| 7 | Schmidt-Hieber (2020) `Nonparametric Regression Using Deep Neural Networks with ReLU Activation Function', The Annals of Statistics 48(4), 1875–1897 | 0.644 | 2 | 2 | 100% |
| 8 | Andreasen, Engsted, Mller \ Sander (2020) `The Yield Spread and Bond Return Predictability in Expansions and Recessions', The Review of Financial Studies 34(6), 2773–2812 | 0.511 | 2 | 1 | 100% |
| 9 | Kohler \ Krzyźak (2017) `Nonparametric regression based on hierarchical interaction models', IEEE Transactions on Information Theory 63(3), 341–356 | 0.511 | 2 | 1 | 100% |
| 10 | Ludvigson \ Ng (2009) `Macro Factors in Bond Risk Premia', The Review of Financial Studies 22(12), 5027–5067 | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 42 scored citations.