arXiv 6 Jun 2023 · Mathematics — Statistics Theory
arXiv:2306.03816 · PDF · DOI · OpenAlex · Extracted main text
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.
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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 | V. Chernozhukov, D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W.… (2018) Double/debiased machine learning for treatment and structural parameters | 1.000 | 5 | 3 | 100% |
| 2 | P. M. Robinson (1988) Root-n-consistent semiparametric regression | 0.950 | 7 | 4 | 86% |
| 3 | I. Castillo (2012) Semiparametric bernstein–von mises theorem and bias, illustrated with gaussian process priors | 0.874 | 5 | 2 | 100% |
| 4 | C. Gourieroux, A. Monfort, and A. Trognon (1984) Pseudo maximum likelihood methods: Theory | 0.874 | 5 | 2 | 100% |
| 5 | P. J. Bickel and B. J. K. Kleijn (2012) The semiparametric Bernstein–von Mises theorem | 0.843 | 4 | 4 | 75% |
| 6 | I. Castillo (2012) A semiparametric bernstein–von mises theorem for gaussian process priors | 0.843 | 10 | 4 | 60% |
| 7 | D. W. K. Andrews (1994) Asymptotics for semiparametric econometric models via stochastic equicontinuity | 0.843 | 3 | 3 | 100% |
| 8 | S. A. Murphy and A. W. Van der Vaart (2000) On profile likelihood | 0.843 | 3 | 3 | 100% |
| 9 | E. Giné and R. Nickl (2015) Mathematical Foundations of Infinite-Dimensional Statistical Models | 0.811 | 5 | 2 | 80% |
| 10 | G. Chamberlain (1992) Efficiency bounds for semiparametric regression | 0.811 | 4 | 2 | 100% |
Showing the top 10 of 65 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
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| 1 | Bayesian Double Machine Learning for Causal Inference | 0.511 | 2 | 1 |
| 2 | Semiparametric Bayesian Inference for a Conditional Moment Equality Model | 0.405 | 1 | 1 |
| 3 | Debiased Bayesian Inference for High-dimensional Regression Models | 0.405 | 1 | 1 |
| 4 | Nonparametric Bayesian Policy Learning | 0.405 | 1 | 1 |