Partially linear single index models for repeated measurements

Ma, Shujie; Liang, Hua; Tsai, Chih‐Ling

doi:10.1016/j.jmva.2014.06.011

Cited by 23 publications

(12 citation statements)

References 42 publications

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“…We advocate using a readily available R package, PGEE (Inan and Wang, 2017), for the linear high-dimensional penalized longitudinal model and show promising results in our numerical study. (Ma et al 2014). In practice one may fix the number of knots when it is not very critical (e.g.…”

Section: An Efficient Algorithmmentioning

confidence: 99%

“…Selection criteria for the number of interior knots for the B-spline basis is based on a variety of approaches. As explained in Ma et al (2014), the number of knots can be chosen by a BIC type criteria focusing on consistency or AIC and cross-validation approaches when efficiency is of interest (He et al, 2002). In Ruppert and Carroll (2000) and Yu and Ruppert (2002), the number of knots implemented depends on the characteristics and shape of the function to be estimated.…”

Section: Spline Smoothing Tuning Parametersmentioning

confidence: 99%

“…Huang et al (2010) claim that when the number of knots does not greatly influence performance, one can fix the amount of knots. Regarding the choice of degree, in practice, usually quadratic and cubic splines are implemented (Ma et al, 2014;Yu et al, 2017). In this study, we use quadratic splines for our simulation analysis and for the CCI-779 study.…”

Section: Spline Smoothing Tuning Parametersmentioning

confidence: 99%

“…linear single-index models, a handful of works have proposed research employing both procedures together, for example inBai et al (2009),Ma et al (2014),Lai et al (2013), andLi et al (2015). However, all of these works assume the dimension of both the singleindex and partially linear covariates is fixed.…”

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confidence: 99%

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Ultra high‐dimensional semiparametric longitudinal data analysis

Green

Lian

et al. 2020

Biometrics

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As ultra-high dimensional longitudinal data is becoming ever more apparent in fields such as public health, information systems, and bioinformatics, developing flexible methods with a sparse set of important variables is of high interest. In this setting, the dimension of the covariates can potentially grow exponentially with respect to the number of clusters. This dissertation research considers a flexible semiparametric approach, namely, partially linear single-index models, for ultra-high dimensional longitudinal data. Most importantly, we allow not only the partially linear covariates, but also the single-index covariates within the unknown flexible function estimated nonparametrically to be ultrahigh dimensional. Using penalized generalized estimating equations, this approach can capture correlation within subjects, can perform simultaneous variable selection and estimation with a smoothly clipped absolute deviation penalty, and can capture nonlinearity and potentially some interactions among predictors. We establish asymptotic theory for the estimators including the oracle property in ultra-high dimension for both the partially linear and nonparametric components. An efficient algorithm is presented to handle the computational challenges, and we show the effectiveness of our method and algorithm via a simulation study and yeast cell cycle gene expression data. In addition, we develop an alternative solution methodology via the penalized quadratic inference function with partially linear single-index models for ultra-high dimensional longitudinal data. This methodology can improve the estimation efficiency when the working correlation structure is misspecified. Performance is demonstrated via a simulation study and analysis of a genomic dataset.

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Section: An Efficient Algorithmmentioning

confidence: 99%

Section: Spline Smoothing Tuning Parametersmentioning

confidence: 99%

Section: Spline Smoothing Tuning Parametersmentioning

confidence: 99%

mentioning

confidence: 99%

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Ultra high‐dimensional semiparametric longitudinal data analysis

Green

Lian

et al. 2020

Biometrics

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“…After surveying some papers on quadratic inference functions, some of which are on the “diverging p ” and/or semiparametric case, we find that this problem is usually addressed in one of the following ways. Explicitly or implicitly (without explicitly stating it as one of the assumptions) assume C ( β ) and/or E [ C ( β )] has eigenvalues bounded and bounded away from zero (Qu et al ; Bai et al ; Lai et al ). Assume the Hessian of Q ( β ) has eigenvalues bounded and bounded away from zero (this also implicitly assumes C is invertible in the first place; otherwise, Q cannot even be defined) (Cho and Qu, ). Assume the p × p K matrix

{[{boldM}_{1}^{T}, \dots, {boldM}_{K}^{T}]}^{T}

has singular values bounded and bounded away from zero (Xue et al ; Wang et al ). Assume all M k , 1⩽ k ⩽ K , have eigenvalues bounded and bounded away from zero (Ma et al ). …”

Section: Introductionmentioning

confidence: 99%

On invertibility of the C‐matrix in quadratic inference functions

Lian

2016

Stat

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A quadratic inference function is often applied to correlated data, with the advantages that it does not involve direct estimation of the correlation parameter and it is more efficient than using generalized estimating equations when the correlation is misspecified. The C‐matrix is used in the definition of a quadratic inference function and is required to be invertible. In this paper, we investigate carefully the question about when the C‐matrix is invertible, which turns out to be non‐trivial. Such a study is missing in the current literature and is especially interesting in a “diverging p” setting where the invertibility of C‐matrix is less clear. Copyright © 2016 John Wiley & Sons, Ltd.

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