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Title: Bootstrap inference for quantile-based modal regression Authors:  Kengo Kato - Cornell University (United States) [presenting]
David Ruppert - Cornell University (United States)
Tao Zhang - Cornell University (United States)
Abstract: Uniform inference methods are developed for the conditional mode based on quantile regression. Specifically, we propose to estimate the conditional mode by minimizing the derivative of the estimated conditional quantile function defined by smoothing the linear quantile regression estimator, and develop two bootstrap methods, a novel pivotal bootstrap and the nonparametric bootstrap, for our conditional mode estimator. Building on high dimensional Gaussian approximation techniques, we establish the validity of simultaneous confidence rectangles constructed from the two bootstrap methods for the conditional mode. We also extend the preceding analysis to the case where the dimension of the covariate vector is increasing with the sample size.