Simultaneous confidence interval for quantile regression

초록

This paper considers a problem of constructing simultaneous confidence intervals for quantile regression. Recently, Krivobokova et al. (J Am Stat Assoc 105: 852-863, 2010) provided simultaneous confidence intervals for penalized spline estimator. However, it is well known that the conventional mean-based penalized spline and its confidence intervals collapse when data are not normally distributed such as skewed or heavy-tailed, and hence, the resultant confidence intervals further provide low coverage probability. To overcome this problem, this paper proposes a new approach that constructs simultaneous confidence intervals for penalized quantile spline estimator, which yields a desired coverage probability. The results obtained from numerical experiments and real data validate the effectiveness of the proposed method.

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