A lack-of-fit test for quantile regression models with high-dimensional covariates

Conde-Amboage, Mercedes; Sellero, César Andrés Sánchez; González–Manteiga, Wenceslao

doi:10.1016/j.csda.2015.02.016

Cited by 19 publications

(27 citation statements)

References 19 publications

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“…It is of interest to define its Cramér‐von Mises version:

\int_{{double-struckS}^{p - 1}} \int_{- \infty}^{\infty} {{\overset{F}{true}}_{S, b} false(x false) - {\overset{F}{true}}_{S^{normalc}, b} false(x false)}^{2} d {\overset{F}{true}}_{b} false(x false) d μ false(b false),

which is equivalent to the test statistic in Conde‐Amboage et al . (). This paper will focus on the Cramér‐type statistic T 1 n since the Cramér test is usually more powerful than the Cramér–von Mises test (Baringhaus and Franz, ), and it is also easier to calculate the value of T 1 n .…”

Section: Lack‐of‐fit Test For Low Dimensional Datamentioning

confidence: 97%

“…For comparison, we also conduct another two tests: the test in Conde‐Amboage et al . (), hence denoted by CSG, and an oracle test, which refers to

{\overset{false^}{T}}_{2 n}

with the sparsity structure being known in advance.…”

Section: Simulation Studiesmentioning

confidence: 99%

“…We also computed the test in Conde‐Amboage et al . (), CSG, for comparison, and the p ‐values are summarized in Table . It can be seen that all p ‐values of

{\overset{false^}{T}}_{2 n}

are smaller than 5%, and then the fitted model fails to provide a good fit to the data.…”

Section: Empirical Analysismentioning

confidence: 99%

“…Conde‐Amboage et al . () suggested projecting the covariates X into a random variable first, and then applying He and Zhu's (2003) method to form a lack‐of‐fit test. It works well for a larger p < n .…”

Section: Introductionmentioning

confidence: 99%

“…As a cost, the number of covariates p is limited to a small value, say 1 or 2, in real applications. Conde-Amboage et al (2015) suggested projecting the covariates X into a random variable first, and then applying He and Zhu's (2003) method to form a lack-of-fit test. It works well for a larger p < n.…”

Section: Introductionmentioning

confidence: 99%

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Lack-of-Fit Tests for Quantile Regression Models

Dong

Feng

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary The paper novelly transforms lack‐of‐fit tests for parametric quantile regression models into checking the equality of two conditional distributions of covariates. Accordingly, by applying some successful two‐sample test statistics in the literature, two tests are constructed to check the lack of fit for low and high dimensional quantile regression models. The low dimensional test works well when the number of covariates is moderate, whereas the high dimensional test can maintain the power when the number of covariates exceeds the sample size. The null distribution of the high dimensional test has an explicit form, and the p‐values or critical values can then be calculated directly. The finite sample performance of the tests proposed is examined by simulation studies, and their usefulness is further illustrated by two real examples.

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“…It is of interest to define its Cramér‐von Mises version:

\int_{{double-struckS}^{p - 1}} \int_{- \infty}^{\infty} {{\overset{F}{true}}_{S, b} false(x false) - {\overset{F}{true}}_{S^{normalc}, b} false(x false)}^{2} d {\overset{F}{true}}_{b} false(x false) d μ false(b false),

Section: Lack‐of‐fit Test For Low Dimensional Datamentioning

confidence: 97%

“…For comparison, we also conduct another two tests: the test in Conde‐Amboage et al . (), hence denoted by CSG, and an oracle test, which refers to

{\overset{false^}{T}}_{2 n}

with the sparsity structure being known in advance.…”

Section: Simulation Studiesmentioning

confidence: 99%

“…We also computed the test in Conde‐Amboage et al . (), CSG, for comparison, and the p ‐values are summarized in Table . It can be seen that all p ‐values of

{\overset{false^}{T}}_{2 n}

are smaller than 5%, and then the fitted model fails to provide a good fit to the data.…”

Section: Empirical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Lack-of-Fit Tests for Quantile Regression Models

Dong

Feng

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Model checking for parametric single‐index quantile models

Yuan

Liu

et al. 2020

Stat

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In this work, we construct a lack‐of‐fit test for testing parametric single‐index quantile regression models. We apply the kernel smoothing technique for the multivariate nonparametric estimation involved in this task. To avoid the “curse of dimensionality” in multivariate nonparametric estimation and to fully utilize the information contained in the model, we employ a sufficient dimension reduction technique to identify the corresponding dimensionally reduced subspace and then construct our test statistic in this subspace. At different quantile levels, the test statistics given in this paper can quickly detect local alternative hypotheses, which are different from the null hypothesis for small and moderate sample sizes. A new wild bootstrap method is applied to approximate the critical values of the quantile regression model test. The effectiveness of the method is verified by simulation experiments and a real data application.

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Powerful nonparametric checks for parametric single‐index quantile models with missing responses

Yuan

Liu

et al. 2022

Stat

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This paper considers the lack‐of‐fit test of parametric single‐index quantile models when the response variable is missing at random. The model's coefficients are estimated by an estimation method suitable for the quantile regression coefficients of the missing data. Simultaneously, an algorithm for solving the central subspace of the multidimensional quantile regression model with missing responses is proposed. Based on the central quantile regression subspace, we construct two‐dimensional reduction adaptive‐to‐model test statistics suitable for randomly missing response variables to avoid the curse of dimensionality. Under the null hypothesis and local alternative hypothesis, the asymptotic properties of the test statistics are obtained. The proposed testing methods are shown to be consistent and able to detect local alternative hypothetical models converging to the null model at the rate of order Ofalse(n−1false/2h−1false/4false). A consistent bootstrap method is proposed to determine the critical values, and its asymptotic properties are established. The simulation results show that the proposed method is superior to existing methods in terms of both empirical size and power in the case of multidimensional and even high‐dimensional covariables. The ACTG Protocol 175 data set is analyzed to demonstrate the application of the testing procedures. Supplementary materials for this article are available online.

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A lack-of-fit test for quantile regression models with high-dimensional covariates

Cited by 19 publications

References 19 publications

Lack-of-Fit Tests for Quantile Regression Models

Lack-of-Fit Tests for Quantile Regression Models

Model checking for parametric single‐index quantile models

Powerful nonparametric checks for parametric single‐index quantile models with missing responses

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