Simultaneous confidence band for single-index random effects models with longitudinal data

Yang, Suigen; Xue, Liugen; Li, Gaorong

doi:10.1016/j.spl.2013.10.014

Cited by 6 publications

(3 citation statements)

References 30 publications

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“…Cui, Härdle & Zhu (2011) introduced the estimating function method to study the single-index models. Pang & Xue (2012) and Yang, Xue & Li (2014) investigated the single-index random effects models with longitudinal data. Li, Peng, Dong & Tong (2014) constructed the simultaneous confidence bands for the nonparametric link function in single-index models.…”

Section: Introductionmentioning

confidence: 99%

SIMEX estimation for single-index model with covariate measurement error

Yang

Tong

2018

AStA Adv Stat Anal

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In this paper, we consider the single-index measurement error model with mismeasured covariates in the nonparametric part. To solve the problem, we develop a simulation-extrapolation (SIMEX) algorithm based on the local linear smoother and the estimating equation. For the proposed SIMEX estimation, it is not needed to assume the distribution of the unobserved covariate. We transform the boundary of a unit ball in R p to the interior of a unit ball in R p−1 by using the constraint β = 1. The proposed SIMEX estimator of the index parameter is shown to be asymptotically normal under some regularity conditions. We also derive the asymptotic bias and variance of the estimator of the unknown link function. Finally, the performance of the proposed method is examined by simulation studies and is illustrated by a real data example.

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Section: Introductionmentioning

confidence: 99%

SIMEX estimation for single-index model with covariate measurement error

Yang

Tong

2018

AStA Adv Stat Anal

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“…Pang and Xue [2] considered estimators of parameters and non-parameter for model (1). Yang et al [3] considered simultaneous confidence band for the model (1).…”

Section: Introductionmentioning

confidence: 99%

“…Since the single-index models are popular and efficient modeling tools in multivariate nonparametric regression, the single-index models have recently received much attention, including those from Carroll et al [4], Xia et al [5], Zhu and Xue [6], Wang et al [7], and among others. Pang and Xue [2], Yang et al [3] and Chen et al [8] considered the single-index models for longitudinal/panel data. Further, random effects models have become very popular for the analysis of longitudinal or panel data, because they are flexible and widely applicable.…”

Section: Introductionmentioning

confidence: 99%

Automatic Variable Selection for Single-Index Random Effects Models with Longitudinal Data

Yang¹,

Xue²

2014

OJS

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We consider the problem of variable selection for the single-index random effects models with longitudinal data. An automatic variable selection procedure is developed using smooth-threshold. The proposed method shares some of the desired features of existing variable selection methods: the resulting estimator enjoys the oracle property; the proposed procedure avoids the convex optimization problem and is flexible and easy to implement. Moreover, we use the penalized weighted deviance criterion for a data-driven choice of the tuning parameters. Simulation studies are carried out to assess the performance of our method, and a real dataset is analyzed for further illustration.

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