Integrated conditional moment test and beyond: when the number of covariates is divergent

Using crowd-source based features from social media and conventional features to predict the movies popularity

Falong Tan and Lixing Zhu

Biometrika, 2022, vol. 109, issue 1, 103-122

Abstract: SummaryThe classical integrated conditional moment test is a promising method for model checking and its basic idea has been applied to develop several variants. However, in diverging-dimension scenarios, the integrated conditional moment test may break down and has completely different limiting properties from the fixed-dimension case. Furthermore, the related wild bootstrap approximation can also be invalid. To extend this classical test to diverging dimension settings, we propose a projected adaptive-to-model version of the integrated conditional moment test. We study the asymptotic properties of the new test under both the null and alternative hypotheses to examine if it maintains significance level, and its sensitivity to the global and local alternatives that are distinct from the null at the rate . The corresponding wild bootstrap approximation can still work for the new test in diverging-dimension scenarios. We also derive the consistency and asymptotically linear representation of the least squares estimator when the parameter diverges at the fastest possible known rate in the literature. Numerical studies show that the new test can greatly enhance the performance of the integrated conditional moment test in high-dimensional cases. We also apply the test to a real dataset for illustration.

Keywords: Adaptive-to-model test; Dimension reduction; Integrated conditional moment test; Least squares estimation; Model checking; Wild bootstrap (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1093/biomet/asab009 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:109:y:2022:i:1:p:103-122.

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Biometrika is currently edited by Paul Fearnhead

More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK.
Bibliographic data for series maintained by Oxford University Press ().