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arXiv · 1511.00273

Calibrated Percentile Double Bootstrap For Robust Linear Regression Inference

Daniel McCarthy·Kai Zhang·Lawrence Brown·Richard Berk·Andreas Buja·Edward George·Linda Zhao
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Abstract

We consider inference for the parameters of a linear model when the covariates are random and the relationship between response and covariates is possibly non-linear. Conventional inference methods such as z-intervals perform poorly in these cases. We propose a double bootstrap-based calibrated percentile method, perc-cal, as a general-purpose CI method which performs very well relative to alternative methods in challenging situations such as these. The superior performance of perc-cal is demonstrated by a thorough, full-factorial design synthetic data study as well as a real data example involving the length of criminal sentences. We also provide theoretical justification for the perc-cal method under mild conditions. The method is implemented in the R package `perccal', available through CRAN and coded primarily in C++, to make it easier for practitioners to use.

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Daniel McCarthy, Kai Zhang, Lawrence Brown, Richard Berk, Andreas Buja, Edward George, Linda Zhao. 2017-01-16. Calibrated Percentile Double Bootstrap For Robust Linear Regression Inference. https://arxiv.org/abs/1511.00273

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