Parametrization, Prior Independence, and the Semiparametric Bernstein-von Mises Theorem for the Partially Linear Model

Christopher D. Walker

Papers from arXiv.org

Abstract: I prove a semiparametric Bernstein-von Mises theorem for a partially linear regression model with independent priors for the low-dimensional parameter of interest and the infinite-dimensional nuisance parameters. My result avoids a challenging prior invariance condition that arises from a loss of information associated with not knowing the nuisance parameter. The key idea is to employ a feasible reparametrization of the partially linear regression model that reflects the semiparametric structure of the model. This allows a researcher to assume independent priors for the model parameters while automatically accounting for the loss of information associated with not knowing the nuisance parameters. The theorem is verified for uniform wavelet series priors and Mat\'{e}rn Gaussian process priors.

Date: 2023-06, Revised 2025-04
New Economics Papers: this item is included in nep-ecm and nep-mfd
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://arxiv.org/pdf/2306.03816 Latest version (application/pdf)

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:arx:papers:2306.03816

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().