Theory and computational tool for interval estimation in linear regressions under heteroscedasticity of unknown form using double bootstrap methods

Pedro Rafael D. Marinho, Francisco Cribari-Neto and Vera Tomazella

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 24, 7986-8013

Abstract: Linear regression models are widely used due to their simplicity and interpretability. However, the assumption of homoscedasticity (constant error variance) is often violated in practice, complicating inference. This article introduces two double bootstrap strategies—the double percentile bootstrap and the double bootstrap-t—to construct interval estimates for regression coefficients under heteroscedasticity of unknown form. The double percentile bootstrap is straightforward to implement and avoids reliance on explicit covariance matrix estimates, while the double bootstrap-t incorporates heteroscedasticity-consistent covariance matrix estimators to enhance precision. Using extensive Monte Carlo simulations, we show that both methods outperform conventional single-bootstrap approaches in maintaining nominal coverage probabilities, with the double bootstrap-t offering superior accuracy in small samples. An empirical application further illustrates the practical benefits of these methods. Additionally, we provide an open-source R package, hcci, enabling researchers to implement these algorithms effectively.

Date: 2025
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DOI: 10.1080/03610926.2025.2486538

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