JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1092 10.6339/23-JDS1092 Statistical Data Science Impact of Bias Correction of the Least Squares Estimation on Bootstrap Confidence Intervals for Bifurcating Autoregressive Models ElbayoumiTamer1 https://orcid.org/0000-0002-8113-702X MostafaSayedsabdelmegeed@ncat.edu1∗ Department of Mathematics & Statistics, North Carolina A&T State University, USA Corresponding author. Email: sabdelmegeed@ncat.edu. 202424220232212544 Supplementary Material

The supplementary material includes the following files and folders: (1) README: a brief explanation of all the files and folders in the supplementary material; (2) The application datasets; (3) Code files; and (4) Additional simulation results.

71020221922023 2024 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2024 Open access article under the CC BY license.

The least squares (LS) estimator of the autoregressive coefficient in the bifurcating autoregressive (BAR) model was recently shown to suffer from substantial bias, especially for small to moderate samples. This study investigates the impact of the bias in the LS estimator on the behavior of various types of bootstrap confidence intervals for the autoregressive coefficient and introduces methods for constructing bias-corrected bootstrap confidence intervals. We first describe several bootstrap confidence interval procedures for the autoregressive coefficient of the BAR model and present their bias-corrected versions. The behavior of uncorrected and corrected confidence interval procedures is studied empirically through extensive Monte Carlo simulations and two real cell lineage data applications. The empirical results show that the bias in the LS estimator can have a significant negative impact on the behavior of bootstrap confidence intervals and that bias correction can significantly improve the performance of bootstrap confidence intervals in terms of coverage, width, and symmetry.

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