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<p>In this paper, we investigate the partially functional linear smoothed quantile regression model, where the responses are censored and the predictors involve both the multiple functional covariates as well as the ultrahigh-dimensional scalar covariates. First, we propose a weighted penalized convolution-type smoothed quantile regression (WPCSQR) method for the estimation and the variable selection of the model, and construct the estimators for both the slope functions and the scalar parameters. Second, we establish the asymptotic properties of the proposed estimators under some mild conditions. Third, we further study the predictions for the conditional quantile function of the response and obtain the convergence rate of the predicted value given the predictors. Fourth, we propose a multiplier bootstrap method based on the censored responses to construct the interval estimators for the important scalar parameters of the model. Finally, some Monte Carlo simulations and an application to the Alzheimer’s Disease Neuroimaging Initiative (ADNI) real data set are carried out to show the effectiveness of the method.</p>

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Smoothed quantile regression for functional partially linear model with ultrahigh-dimensions and censored responses

  • 期刊论文

  • 发表日期：

    2026年1月27日

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  • Chengxin Wu,
  • Nengxiang Ling

摘要

In this paper, we investigate the partially functional linear smoothed quantile regression model, where the responses are censored and the predictors involve both the multiple functional covariates as well as the ultrahigh-dimensional scalar covariates. First, we propose a weighted penalized convolution-type smoothed quantile regression (WPCSQR) method for the estimation and the variable selection of the model, and construct the estimators for both the slope functions and the scalar parameters. Second, we establish the asymptotic properties of the proposed estimators under some mild conditions. Third, we further study the predictions for the conditional quantile function of the response and obtain the convergence rate of the predicted value given the predictors. Fourth, we propose a multiplier bootstrap method based on the censored responses to construct the interval estimators for the important scalar parameters of the model. Finally, some Monte Carlo simulations and an application to the Alzheimer’s Disease Neuroimaging Initiative (ADNI) real data set are carried out to show the effectiveness of the method.