Varying Index Coefficient Models

Ma, Shujie; Song, Peter X.‐K.

doi:10.1080/01621459.2014.903185

Cited by 68 publications

(52 citation statements)

References 51 publications

(42 reference statements)

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“…Given the n 1/2 -consistent parametric estimates and consistent nonparametric functions estimates, a two-step spline backfitted local linear modal estimation can be obtained for achieving the asymptotic normalities of the nonparametric functions. The simulation results show that the proposed procedures are robust to outliers and efficient to heavy-tailed distribution, and perform almost as well as that of Ma and Song (2014) for the normal error distribution.…”

Section: Introductionmentioning

confidence: 67%

“…In this paper, we consider the following VICMs proposed by Ma and Song (2014) which are given as follows: …”

Section: Introductionmentioning

confidence: 99%

“…For example, the VICM can be used to model and assess nonlinear interaction effects between grouped covariates and the response variable. The details about the relationship of the VICM to the existing models and properties of the VICM can refer to Ma and Song (2014).…”

Section: Introductionmentioning

confidence: 99%

“…Although model (1) is natural and useful in many practical applications, the literature on this model is very limited since the VICM is a new and complicated semiparametric model which involves multiple nonparametric functions simultaneously. So far, only the profile least squares method was proposed to estimate the loading coefficient vectors β l and a two-step spline backfitted local linear regression method was used to estimate the nonparametric functions m l (·) (Ma and Song 2014). Although the profile least squares and local linear fitting are computationally fast estimation procedures since they have the analytic solution, they are expected to be very sensitive to outliers and their efficiency may be significantly reduced for many commonly used non-normal errors.…”

Section: Introductionmentioning

confidence: 99%

“…Following Ma and Song (2014), we use basis approximations to estimate the nonparametric functions. That is, we approximate m l (·) by B-spline basis functions because they have bounded support and are numerically stable (Schumaker 1981).…”

Section: Introductionmentioning

confidence: 99%

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Robust estimation for varying index coefficient models

Yang

Guo

2015

Comput Stat

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Varying index coefficient models (VICMs) proposed by Ma and Song (J Am Stat Assoc, 2014. ) are a new class of semiparametric models, which encompass most of the existing semiparametric models. So far, only the profile least squares method and local linear fitting were developed for the VICM, which are very sensitive to the outliers and will lose efficiency for the heavy tailed error distributions. In this paper, we propose an efficient and robust estimation procedure for the VICM based on modal regression which depends on a bandwidth. We establish the consistency and asymptotic normality of proposed estimators for index coefficients by utilizing profile spline modal regression method. The oracle property of estimators for the nonparametric functions is also established by utilizing a two-step spline backfitted local linear modal regression approach. In addition, we discuss the bandwidth selection for achieving better robustness and efficiency and propose a modified expectation-maximization-type algorithm for the proposed estimation procedure. Finally, simulation studies and a real data analysis are carried out to assess the finite sample performance of the proposed method.

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Section: Introductionmentioning

confidence: 67%

“…In this paper, we consider the following VICMs proposed by Ma and Song (2014) which are given as follows: …”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust estimation for varying index coefficient models

Yang

Guo

2015

Comput Stat

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svReg: Structural varying‐coefficient regression to differentiate how regional brain atrophy affects motor impairment for Huntington disease severity groups

2021

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For Huntington disease, identification of brain regions related to motor impairment can be useful for developing interventions to alleviate the motor symptom, the major symptom of the disease. However, the effects from the brain regions to motor impairment may vary for different groups of patients. Hence, our interest is not only to identify the brain regions but also to understand how their effects on motor impairment differ by patient groups. This can be cast as a model selection problem for a varying‐coefficient regression. However, this is challenging when there is a pre‐specified group structure among variables. We propose a novel variable selection method for a varying‐coefficient regression with such structured variables and provide a publicly available R package svreg for implementation of our method. Our method is empirically shown to select relevant variables consistently. Also, our method screens irrelevant variables better than existing methods. Hence, our method leads to a model with higher sensitivity, lower false discovery rate and higher prediction accuracy than the existing methods. Finally, we found that the effects from the brain regions to motor impairment differ by disease severity of the patients. To the best of our knowledge, our study is the first to identify such interaction effects between the disease severity and brain regions, which indicates the need for customized intervention by disease severity.

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Evaluating functional covariate‐environment interactions in the Cox regression model

Zhou

Lin

et al. 2019

Can J Statistics

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Children exposed to mixtures of endocrine disrupting compounds such as phthalates are at high risk of experiencing significant friction in their growth and sexual maturation. This article is primarily motivated by a study that aims to assess the toxicants‐modified effects of risk factors related to the hazards of early or delayed onset of puberty among children living in Mexico City. To address the hypothesis of potential nonlinear modification of covariate effects, we propose a new Cox regression model with multiple functional covariate‐environment interactions, which allows covariate effects to be altered nonlinearly by mixtures of exposed toxicants. This new class of models is rather flexible and includes many existing semiparametric Cox models as special cases. To achieve efficient estimation, we develop the global partial likelihood method of inference, in which we establish key large‐sample results, including estimation consistency, asymptotic normality, semiparametric efficiency and the generalized likelihood ratio test for both parameters and nonparametric functions. The proposed methodology is examined via simulation studies and applied to the analysis of the motivating data, where maternal exposures to phthalates during the third trimester of pregnancy are found to be important risk modifiers for the age of attaining the first stage of puberty. The Canadian Journal of Statistics 47: 204–221; 2019 © 2019 Statistical Society of Canada

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Varying Index Coefficient Models

Cited by 68 publications

References 51 publications

Robust estimation for varying index coefficient models

Robust estimation for varying index coefficient models

svReg: Structural varying‐coefficient regression to differentiate how regional brain atrophy affects motor impairment for Huntington disease severity groups

Evaluating functional covariate‐environment interactions in the Cox regression model

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