<p>In this paper, we study the model specification test for the single-index quantile regression model with randomly right-censored data. In the literature, model checking for parametric quantile regression models rarely accounts for censored cases. Censored quantile regression can not be applied to high-dimensional data directly due to the “curse of dimensionality”. The single-index model can tackle the high-dimensional issue efficiently. We adopt the sufficient dimension reduction technique to identify dimension reduction subspaces and construct test statistics for randomly right censoring response variable. Under mild conditions, we obtain the asymptotic properties of the proposed test. We can readily determine critical values using the limiting null distribution of the proposed test, incurring no significant computational cost. Furthermore, the proposed testing method is consistent and capable of detecting local alternative hypothetical models converging to the null model at a rate of order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$O\bigg (n^{-\frac{1}{2}}h^{-\frac{1}{4}}\bigg )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mrow> <mo maxsize="2.047em" minsize="2.047em" stretchy="true">(</mo> </mrow> <msup> <mi>n</mi> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <msup> <mi>h</mi> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> </msup> <mrow> <mo maxsize="2.047em" minsize="2.047em" stretchy="true">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. We also propose the bootstrap method to obtain the <i>p</i>-value. Monte Carlo simulation results demonstrate that the proposed test maintains its empirical sizes regardless of whether the data is high-dimensional or not. Finally, two real data analyses illustrate the usefulness of the proposed test methodology.</p>

Model checking for parametric single-index quantile regression with randomly right censoring response

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发表日期：

2026年5月27日

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Ruiyun Zhang,
Xiaoyan Zhao,
Yuanyuan Jiang,
Tianfa Xie

摘要

In this paper, we study the model specification test for the single-index quantile regression model with randomly right-censored data. In the literature, model checking for parametric quantile regression models rarely accounts for censored cases. Censored quantile regression can not be applied to high-dimensional data directly due to the “curse of dimensionality”. The single-index model can tackle the high-dimensional issue efficiently. We adopt the sufficient dimension reduction technique to identify dimension reduction subspaces and construct test statistics for randomly right censoring response variable. Under mild conditions, we obtain the asymptotic properties of the proposed test. We can readily determine critical values using the limiting null distribution of the proposed test, incurring no significant computational cost. Furthermore, the proposed testing method is consistent and capable of detecting local alternative hypothetical models converging to the null model at a rate of order $O\bigg (n^{-\frac{1}{2}}h^{-\frac{1}{4}}\bigg )$ $O (n^{- \frac{1}{2}} h^{- \frac{1}{4}})$ . We also propose the bootstrap method to obtain the p-value. Monte Carlo simulation results demonstrate that the proposed test maintains its empirical sizes regardless of whether the data is high-dimensional or not. Finally, two real data analyses illustrate the usefulness of the proposed test methodology.