From Model Selection to Model Averaging: A Comparison for Nested Linear Models

by   Wenchao Xu, et al.

Model selection (MS) and model averaging (MA) are two popular approaches when having many candidate models. Theoretically, the estimation risk of an oracle MA is not larger than that of an oracle MS because the former one is more flexible, but a foundational issue is: does MA offer a substantial improvement over MS? Recently, a seminal work: Peng and Yang (2021), has answered this question under nested models with linear orthonormal series expansion. In the current paper, we further reply this question under linear nested regression models. Especially, a more general nested framework, heteroscedastic and autocorrelated random errors, and sparse coefficients are allowed in the current paper, which is more common in practice. In addition, we further compare MAs with different weight sets. Simulation studies support the theoretical findings in a variety of settings.



page 1

page 2

page 3

page 4


Model Selection of Nested and Non-Nested Item Response Models using Vuong Tests

In this paper, we apply Vuong's (1989) general approach of model selecti...

A generalized EMS algorithm for model selection with incomplete data

Recently, a so-called E-MS algorithm was developed for model selection i...

Nested Model Averaging on Solution Path for High-dimensional Linear Regression

We study the nested model averaging method on the solution path for a hi...

When and when not to use optimal model averaging

Traditionally model averaging has been viewed as an alternative to model...

Optimal designs for model averaging in non-nested models

In this paper we construct optimal designs for frequentist model averagi...

Adaptive α Significance Level for Linear Models

We put forward an adaptive alpha that decreases as the information grows...

Margin-adaptive model selection in statistical learning

A classical condition for fast learning rates is the margin condition, f...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.