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Regression with Variable Dimension Covariates

Author

Listed:
  • Peter Mueller

    (University of Texas at Austin)

  • Fernando Andrés Quintana

    (Pontificia Universidad Católica de Chile)

  • Garritt L. Page

    (Brigham Young University)

Abstract

Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the ubiquitous nature of regression problems and the abundance of related methods and results there is a surprising gap in the literature. There are no well established methods for regression with a varying dimension covariate vectors, despite the common occurrence of such problems. In this paper we review some recent related papers proposing varying dimension regression by way of random partitions.

Suggested Citation

  • Peter Mueller & Fernando Andrés Quintana & Garritt L. Page, 2024. "Regression with Variable Dimension Covariates," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 185-198, November.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00329-3
    DOI: 10.1007/s13171-023-00329-3
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    References listed on IDEAS

    as
    1. Noirrit Kiran Chandra & Abhra Sarkar & John F. de Groot & Ying Yuan & Peter Müller, 2023. "Bayesian Nonparametric Common Atoms Regression for Generating Synthetic Controls in Clinical Trials," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(544), pages 2301-2314, October.
    2. Rina Friedberg & Julie Tibshirani & Susan Athey & Stefan Wager, 2018. "Local Linear Forests," Papers 1807.11408, arXiv.org, revised Sep 2020.
    3. Anirban Bhattacharya & Debdeep Pati & Natesh S. Pillai & David B. Dunson, 2015. "Dirichlet--Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1479-1490, December.
    4. Fernando A. Quintana & Pilar L. Iglesias, 2003. "Bayesian clustering and product partition models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 557-574, May.
    5. J. G. Ibrahim & S. R. Lipsitz & M.‐H. Chen, 1999. "Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 173-190.
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    More about this item

    Keywords

    Density regression; Clustering; Partition; Missing data;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • H51 - Public Economics - - National Government Expenditures and Related Policies - - - Government Expenditures and Health

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