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Bootstrap-quantile ridge estimator for linear regression with applications

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  • Irum Sajjad Dar
  • Sohail Chand

Abstract

Bootstrap is a simple, yet powerful method of estimation based on the concept of random sampling with replacement. The ridge regression using a biasing parameter has become a viable alternative to the ordinary least square regression model for the analysis of data where predictors are collinear. This paper develops a nonparametric bootstrap-quantile approach for the estimation of ridge parameter in the linear regression model. The proposed method is illustrated using some popular and widely used ridge estimators, but this idea can be extended to any ridge estimator. Monte Carlo simulations are carried out to compare the performance of the proposed estimators with their baseline counterparts. It is demonstrated empirically that MSE obtained from our suggested bootstrap-quantile approach are substantially smaller than their baseline estimators especially when collinearity is high. Application to real data sets reveals the suitability of the idea.

Suggested Citation

  • Irum Sajjad Dar & Sohail Chand, 2024. "Bootstrap-quantile ridge estimator for linear regression with applications," PLOS ONE, Public Library of Science, vol. 19(4), pages 1-19, April.
    • Handle: RePEc:plo:pone00:0302221
    DOI: 10.1371/journal.pone.0302221
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    References listed on IDEAS

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    1. Tim C. Hesterberg, 2015. "What Teachers Should Know About the Bootstrap: Resampling in the Undergraduate Statistics Curriculum," The American Statistician, Taylor & Francis Journals, vol. 69(4), pages 371-386, November.
    2. Delaney, Nancy Jo & Chatterjee, Sangit, 1986. "Use of the Bootstrap and Cross-validation in Ridge Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(2), pages 255-262, April.
    3. Issam Dawoud & B. M. Golam Kibria, 2020. "A New Biased Estimator to Combat the Multicollinearity of the Gaussian Linear Regression Model," Stats, MDPI, vol. 3(4), pages 1-16, November.
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