Estimation and Inference for a Class of Generalized Hierarchical Models

Chaohua Dong, Jiti Gao (), Bin Peng () and Yayi Yan

No 7/24, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: 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.

Keywords: Estimation Theory; Deep Neural Network; Hierarchical Model; ReLU (search for similar items in EconPapers)
JEL-codes: C14 C45 G12 (search for similar items in EconPapers)
Pages: 62
Date: 2024
New Economics Papers: this item is included in nep-big and nep-cmp
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