IDEAS home Printed from https://ideas.repec.org/a/gam/jagris/v13y2023i4p826-d1115470.html
   My bibliography  Save this article

Estimation of Error Variance in Genomic Selection for Ultrahigh Dimensional Data

Author

Listed:
  • Sayanti Guha Majumdar

    (Division of Agricultural Bioinformatics, ICAR-Indian Agricultural Statistics Research Institute, New Delhi 110012, India
    These authors contributed equally to this work.)

  • Anil Rai

    (Division of Agricultural Bioinformatics, ICAR-Indian Agricultural Statistics Research Institute, New Delhi 110012, India
    These authors contributed equally to this work.)

  • Dwijesh Chandra Mishra

    (Division of Agricultural Bioinformatics, ICAR-Indian Agricultural Statistics Research Institute, New Delhi 110012, India)

Abstract

Estimation of error variance in the case of genomic selection is a necessary step to measure the accuracy of the genomic selection model. For genomic selection, whole-genome high-density marker data is used where the number of markers is always larger than the sample size. This makes it difficult to estimate the error variance because the ordinary least square estimation technique cannot be used in the case of datasets where the number of parameters is greater than the number of individuals (i.e., p > n ). In this article, two existing methods, viz. Refitted Cross Validation (RCV) and kfold-RCV, were suggested for such cases. Moreover, by considering the limitations of the above methods, two new methods, viz. Bootstrap-RCV and Ensemble method, have been proposed. Furthermore, an R package “varEst” has been developed, which contains four different functions to implement these error variance estimation methods in the case of Least Absolute Shrinkage and Selection Operator (LASSO), Least Squares Regression (LSR) and Sparse Additive Models (SpAM). The performances of the algorithms have been evaluated using simulated and real datasets.

Suggested Citation

  • Sayanti Guha Majumdar & Anil Rai & Dwijesh Chandra Mishra, 2023. "Estimation of Error Variance in Genomic Selection for Ultrahigh Dimensional Data," Agriculture, MDPI, vol. 13(4), pages 1-16, April.
    • Handle: RePEc:gam:jagris:v:13:y:2023:i:4:p:826-:d:1115470
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2077-0472/13/4/826/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2077-0472/13/4/826/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jianqing Fan & Shaojun Guo & Ning Hao, 2012. "Variance estimation using refitted cross‐validation in ultrahigh dimensional regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 37-65, January.
    2. Lee H. Dicker, 2014. "Variance estimation in high-dimensional linear models," Biometrika, Biometrika Trust, vol. 101(2), pages 269-284.
    3. Zhao Chen & Jianqing Fan & Runze Li, 2018. "Error Variance Estimation in Ultrahigh-Dimensional Additive Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 315-327, January.
    4. Zhijian Li & Wei Lin, 2020. "Efficient error variance estimation in non‐parametric regression," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(4), pages 467-484, December.
    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. X Liu & S Zheng & X Feng, 2020. "Estimation of error variance via ridge regression," Biometrika, Biometrika Trust, vol. 107(2), pages 481-488.
    7. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    8. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    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. Xin Wang & Lingchen Kong & Liqun Wang, 2022. "Estimation of Error Variance in Regularized Regression Models via Adaptive Lasso," Mathematics, MDPI, vol. 10(11), pages 1-19, June.
    2. Wang, Luheng & Chen, Zhao & Wang, Christina Dan & Li, Runze, 2020. "Ultrahigh dimensional precision matrix estimation via refitted cross validation," Journal of Econometrics, Elsevier, vol. 215(1), pages 118-130.
    3. Xia Zheng & Yaohua Rong & Ling Liu & Weihu Cheng, 2021. "A More Accurate Estimation of Semiparametric Logistic Regression," Mathematics, MDPI, vol. 9(19), pages 1-12, September.
    4. Yi Liu & Veronika Ročková & Yuexi Wang, 2021. "Variable selection with ABC Bayesian forests," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 453-481, July.
    5. Bhatnagar, Sahir R. & Lu, Tianyuan & Lovato, Amanda & Olds, David L. & Kobor, Michael S. & Meaney, Michael J. & O'Donnell, Kieran & Yang, Archer Y. & Greenwood, Celia M.T., 2023. "A sparse additive model for high-dimensional interactions with an exposure variable," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    6. Hyung Park & Thaddeus Tarpey & Eva Petkova & R. Todd Ogden, 2024. "A high-dimensional single-index regression for interactions between treatment and covariates," Statistical Papers, Springer, vol. 65(7), pages 4025-4056, September.
    7. Adel Javanmard & Jason D. Lee, 2020. "A flexible framework for hypothesis testing in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 685-718, July.
    8. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    9. Hang Yu & Yuanjia Wang & Donglin Zeng, 2023. "A general framework of nonparametric feature selection in high‐dimensional data," Biometrics, The International Biometric Society, vol. 79(2), pages 951-963, June.
    10. Zhu Wang, 2022. "MM for penalized estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 54-75, March.
    11. Naimoli, Antonio, 2022. "Modelling the persistence of Covid-19 positivity rate in Italy," Socio-Economic Planning Sciences, Elsevier, vol. 82(PA).
    12. Zemin Zheng & Jie Zhang & Yang Li, 2022. "L 0 -Regularized Learning for High-Dimensional Additive Hazards Regression," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2762-2775, September.
    13. Zichen Zhang & Ye Eun Bae & Jonathan R. Bradley & Lang Wu & Chong Wu, 2022. "SUMMIT: An integrative approach for better transcriptomic data imputation improves causal gene identification," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    14. Peter Bühlmann & Jacopo Mandozzi, 2014. "High-dimensional variable screening and bias in subsequent inference, with an empirical comparison," Computational Statistics, Springer, vol. 29(3), pages 407-430, June.
    15. Capanu, Marinela & Giurcanu, Mihai & Begg, Colin B. & Gönen, Mithat, 2023. "Subsampling based variable selection for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    16. Bernardi, Mauro & Costola, Michele, 2019. "High-dimensional sparse financial networks through a regularised regression model," SAFE Working Paper Series 244, Leibniz Institute for Financial Research SAFE.
    17. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    18. Zeyu Bian & Erica E. M. Moodie & Susan M. Shortreed & Sahir Bhatnagar, 2023. "Variable selection in regression‐based estimation of dynamic treatment regimes," Biometrics, The International Biometric Society, vol. 79(2), pages 988-999, June.
    19. Li, Peili & Jiao, Yuling & Lu, Xiliang & Kang, Lican, 2022. "A data-driven line search rule for support recovery in high-dimensional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    20. Wang, Tao & Xu, Pei-Rong & Zhu, Li-Xing, 2012. "Non-convex penalized estimation in high-dimensional models with single-index structure," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 221-235.

    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:gam:jagris:v:13:y:2023:i:4:p:826-:d:1115470. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.