IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v183y2022ics0167715221002868.html
   My bibliography  Save this article

Estimating accuracy of the MCMC variance estimator: Asymptotic normality for batch means estimators

Author

Listed:
  • Chakraborty, Saptarshi
  • Bhattacharya, Suman K.
  • Khare, Kshitij

Abstract

We establish asymptotic normality of the batch means estimator of MCMC variance for reversible geometrically ergodic chains. Existing results use assumptions which are not feasible for most statistical MCMC applications. Practical utility of the result is demonstrated through numerical examples.

Suggested Citation

  • Chakraborty, Saptarshi & Bhattacharya, Suman K. & Khare, Kshitij, 2022. "Estimating accuracy of the MCMC variance estimator: Asymptotic normality for batch means estimators," Statistics & Probability Letters, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:stapro:v:183:y:2022:i:c:s0167715221002868
    DOI: 10.1016/j.spl.2021.109337
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715221002868
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2021.109337?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Halim Damerdji, 1991. "Strong Consistency and Other Properties of the Spectral Variance Estimator," Management Science, INFORMS, vol. 37(11), pages 1424-1440, November.
    2. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    3. David F. Muñoz & Peter W. Glynn, 1997. "A Batch Means Methodology for Estimation of a Nonlinear Function of a Steady-State Mean," Management Science, INFORMS, vol. 43(8), pages 1121-1135, August.
    4. Chiahon Chien & David Goldsman & Benjamin Melamed, 1997. "Large-Sample Results for Batch Means," Management Science, INFORMS, vol. 43(9), pages 1288-1295, September.
    5. Vivekananda Roy & James P. Hobert, 2007. "Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 607-623, September.
    6. Jones, Galin L. & Haran, Murali & Caffo, Brian S. & Neath, Ronald, 2006. "Fixed-Width Output Analysis for Markov Chain Monte Carlo," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1537-1547, December.
    7. Abdelkamel Alj & Rajae Azrak & Guy Melard, 2014. "On Conditions in Central Limit Theorems for Martingale Difference Arrays Long Version," Working Papers ECARES ECARES 2014-05, ULB -- Universite Libre de Bruxelles.
    8. Alj, Abdelkamel & Azrak, Rajae & Mélard, Guy, 2014. "On conditions in central limit theorems for martingale difference arrays," Economics Letters, Elsevier, vol. 123(3), pages 305-307.
    9. Qin, Qian & Hobert, James P., 2018. "Trace-class Monte Carlo Markov chains for Bayesian multivariate linear regression with non-Gaussian errors," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 335-345.
    10. Dootika Vats & James M Flegal & Galin L Jones, 2019. "Multivariate output analysis for Markov chain Monte Carlo," Biometrika, Biometrika Trust, vol. 106(2), pages 321-337.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ying Liu & Dootika Vats & James M. Flegal, 2022. "Batch Size Selection for Variance Estimators in MCMC," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 65-93, March.
    2. Kin Wai Chan & Chun Yip Yau, 2017. "High-order Corrected Estimator of Asymptotic Variance with Optimal Bandwidth," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 866-898, December.
    3. Johnson, Alicia A. & Jones, Galin L., 2015. "Geometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 325-342.
    4. Rajae Azrak & Guy Mélard, 2022. "Autoregressive Models with Time-Dependent Coefficients—A Comparison between Several Approaches," Stats, MDPI, vol. 5(3), pages 1-21, August.
    5. Rajae Azrak & Guy Mélard, 2021. "Asymptotic properties of conditional least-squares estimators for array time series," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 525-547, October.
    6. Kshitij Khare & Malay Ghosh, 2022. "MCMC Convergence for Global-Local Shrinkage Priors," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 211-234, September.
    7. Quan Zhou & Jun Yang & Dootika Vats & Gareth O. Roberts & Jeffrey S. Rosenthal, 2022. "Dimension‐free mixing for high‐dimensional Bayesian variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1751-1784, November.
    8. Li, Haoxiang & Qin, Qian & Jones, Galin L., 2024. "Convergence analysis of data augmentation algorithms for Bayesian robust multivariate linear regression with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    9. Christos Alexopoulos & Nilay Tanık Argon & David Goldsman & Gamze Tokol & James R. Wilson, 2007. "Overlapping Variance Estimators for Simulation," Operations Research, INFORMS, vol. 55(6), pages 1090-1103, December.
    10. Christos Alexopoulos & David Goldsman & Gamze Tokol, 2001. "Properties of Batched Quadratic-Form Variance Parameter Estimators for Simulations," INFORMS Journal on Computing, INFORMS, vol. 13(2), pages 149-156, May.
    11. Park, Jaewoo & Jin, Ick Hoon & Schweinberger, Michael, 2022. "Bayesian model selection for high-dimensional Ising models, with applications to educational data," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    12. Jian, Zhihong & Li, Xupei & Zhu, Zhican, 2020. "Sequential forecasting of downside extreme risk during overnight and daytime: Evidence from the Chinese Stock Market☆," Pacific-Basin Finance Journal, Elsevier, vol. 64(C).
    13. Blöchlinger, Andreas, 2021. "Interest rate risk in the banking book: A closed-form solution for non-maturity deposits," Journal of Banking & Finance, Elsevier, vol. 125(C).
    14. Alex Stivala & Garry Robins & Alessandro Lomi, 2020. "Exponential random graph model parameter estimation for very large directed networks," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-21, January.
    15. Niloy Biswas & Anirban Bhattacharya & Pierre E. Jacob & James E. Johndrow, 2022. "Coupling‐based convergence assessment of some Gibbs samplers for high‐dimensional Bayesian regression with shrinkage priors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 973-996, July.
    16. Li, Chunyu & Lou, Chenxin & Luo, Dan & Xing, Kai, 2021. "Chinese corporate distress prediction using LASSO: The role of earnings management," International Review of Financial Analysis, Elsevier, vol. 76(C).
    17. Lada, Emily K. & Wilson, James R., 2006. "A wavelet-based spectral procedure for steady-state simulation analysis," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1769-1801, November.
    18. Riccardo (Jack) Lucchetti & Luca Pedini, 2020. "ParMA: Parallelised Bayesian Model Averaging for Generalised Linear Models," Working Papers 2020:28, Department of Economics, University of Venice "Ca' Foscari".
    19. Armagan, Artin & Dunson, David, 2011. "Sparse variational analysis of linear mixed models for large data sets," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1056-1062, August.
    20. Joshua Chan & Arnaud Doucet & Roberto León-González & Rodney W. Strachan, 2018. "Multivariate Stochastic Volatility with Co-Heteroscedasticity," Working Paper series 18-38, Rimini Centre for Economic Analysis.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:183:y:2022:i:c:s0167715221002868. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.