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Register a new userBootstrap inference for quantile-based modal regression
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Added by
Tao Zhang
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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In this paper, we develop uniform inference methods 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. Finally, we conduct simulation experiments and a real data analysis using U.S. wage data to demonstrate the finite sample performance of our inference method.
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In the fields of clinical trials, biomedical surveys, marketing, banking, with dichotomous response variable, the logistic regression is considered as an alternative convenient approach to linear regression. In this paper, we develop a novel bootstrap technique based on perturbation resampling method for approximating the distribution of the maximum likelihood estimator (MLE) of the regression parameter vector. We establish second order correctness of the proposed bootstrap method after proper studentization and smoothing. It is shown that inferences drawn based on the proposed bootstrap method are more accurate compared to that based on asymptotic normality. The main challenge in establishing second order correctness remains in the fact that the response variable being binary, the resulting MLE has a lattice structure. We show the direct bootstrapping approach fails even after studentization. We adopt smoothing technique developed in Lahiri (1993) to ensure that the smoothed studentized version of the MLE has a density. Similar smoothing strategy is employed to the bootstrap version also to achieve second order correct approximation.
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