Quantile regression in varying-coefficient models: non-crossing quantile curves and heteroscedasticity

Andriyana, Yudhie; Gijbels, Irène; Verhasselt, Anneleen

doi:10.1007/s00362-016-0847-7

Cited by 19 publications

(22 citation statements)

References 37 publications

(33 reference statements)

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“…Estimating all the components simultaneously can be tricky (due to identifiability issues). We use the Adaptive He (AHe) approach (Andriyana and Gijbels 2016; Andriyana, Gijbels, and Verhasselt 2016;Gijbels et al 2016) to deal with the identifiability problem. This approach has two advantages: it avoids crossings of the estimated quantile regression curves when estimating several quantiles and the variability function can be estimated.…”

Section: Estimation Methodsmentioning

confidence: 99%

Shape testing in quantile varying coefficient models with heteroscedastic error

Gijbels

Ibrahim

Verhasselt

2017

Journal of Nonparametric Statistics

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The interest is in regression quantiles in varying coefficient models for analyzing longitudinal data. The coefficients are allowed to vary with time, and the error variance (the variability function) varies with the covariates to allow for heteroscedasticity. The functional coefficients are estimated using penalized splines (P-splines), not requiring specification of the error distribution. A likelihood-ratio-type test is considered to test the shape (constancy, monotonicity and/or convexity) of the functional coefficients. Further, testing procedures based on L1-norm, L2-norm and L∞-norm of the differences of the P-splines coefficients are considered to test for constant functional coefficients. These norm based tests perform better than the likelihood-ratio-type test in our simulation study. An extreme value test for testing monotonicity or convexity, also performs better than the likelihood-ratio-type test. The likelihood-ratio-type test is, however, useful when testing the shape of the coefficients in signal and in variability function simultaneously. A real data example demonstrates the testing procedures.

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Section: Estimation Methodsmentioning

confidence: 99%

Shape testing in quantile varying coefficient models with heteroscedastic error

Gijbels

Ibrahim

Verhasselt

2017

Journal of Nonparametric Statistics

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“…We say that structure

V_{1}

is nested in

V_{2}

(denoted hereafter as

V_{1} \subseteq V_{2}

V_{2}

is “nested” (in an approximative sense) in

V_{3}

, and

V_{3}

is nested in

V_{4}

. Model

V_{2}

, with

θ = 0

, is considered by Andriyana, Gijbels, & Verhasselt (). A variability function similar to

V_{4}

is considered by Van Keilegom & Wang (), with a partially linear structure.…”

Section: Heteroscedastic Modelmentioning

confidence: 99%

“…The aforementioned variability functions are investigated using an approach similar to that of Andriyana, Gijbels, & Verhasselt (). Such an approach consists of adapting the approach of He () to the context of VCMs, and is therefore termed the “Adaptive He (AHe) approach” in the literature.…”

Section: Estimation Proceduresmentioning

confidence: 99%

“…Hence, it is of interest for investigating the evolvement of an HIV/AIDS infection over time. The simple heteroscedastic model has been previously used (by Andriyana, Gijbels, & Verhasselt ()) with these data and the validity of the two assumptions of the AHe approach checked (and fulfilled). To analyze the data set, B‐splines of degree three with 11 equidistant knots in the time interval and differencing of order one are used.…”

Section: Real Data Examplementioning

confidence: 99%

“…Several smoothing methods are considered in the literature for quantile regression: local polynomial in Chaudhuri (), Honda (), and Cai & Xu (); smoothing splines in He, Ng, & Portnoy (); B‐splines in He & Shi () and Kim (); and penalized B‐splines (P‐splines) in Bollaerts, Eilers, & Aerts () and, Andriyana, Gijbels, & Verhasselt, ; Andriyana, Gijbels, & Verhasselt, . There is also a vast literature on variable selection in VCMs, when the focus is on quantile estimation (e.g., Noh, Chung, & Van Keilegom, ; Tang, Wang, & Zhu, ).…”

Section: Introductionmentioning

confidence: 99%

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Testing the heteroscedastic error structure in quantile varying coefficient models

2017

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In mean regression the characteristic of interest is the conditional mean of the response given the covariates. In quantile regression the aim is to estimate any quantile of the conditional distribution function. For given covariates, the conditional quantile function fully characterizes the entire conditional distribution function, in contrast to the mean which is just one of its characteristic quantities. Regression quantiles substantially out‐perform the least‐squares estimator for a wide class of non‐Gaussian error distributions. In this article we consider quantile varying coefficient models (VCMs) that are an extension of classical quantile linear regression models, in which one allows the coefficients to depend on other variables. We consider VCMs with various structures for the variance of the errors (the variability function) in order to allow for heteroscedasticity. For longitudinal data, the time (T) dependent coefficient functions in the signal and the variability functions are estimated with P‐splines (Penalized B‐splines). Consistency of the proposed estimators is proved. Further, likelihood‐ratio‐type tests are considered for comparing the variability functions. The performance of the testing procedure is illustrated on simulated and real data. The Canadian Journal of Statistics 46: 246–264; 2018 © 2017 Statistical Society of Canada

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Semi-parametric small area inference in generalized semi-varying coefficient mixed effects models

Yang

2016

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We investigate semi-parametric small area inference in generalized semivarying coefficient mixed effects models with application to longitudinal data. Combining the generalized profiled likelihood approaches for mixed effect models with kernel methods, we not only construct semi-parametric small area estimators, but also propose two test statistics for discriminating between a parametric mixed effects model and a generalized semi-varying coefficient mixed effects model. The critical values are estimated by a bootstrap procedure. The asymptotic theory for the methods is provided. Simulations exhibit the finite-sample performance for the proposed estimators and test statistics. These verify the feasibility and the excellent behavior of the methods for moderate sample sizes.

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Quantile regression in varying-coefficient models: non-crossing quantile curves and heteroscedasticity

Cited by 19 publications

References 37 publications

Shape testing in quantile varying coefficient models with heteroscedastic error

Shape testing in quantile varying coefficient models with heteroscedastic error

Testing the heteroscedastic error structure in quantile varying coefficient models

Semi-parametric small area inference in generalized semi-varying coefficient mixed effects models

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