Estimation for the single-index models with random effects

Pang, Zhen; Xue, Liugen

doi:10.1016/j.csda.2011.11.007

Cited by 25 publications

(22 citation statements)

References 38 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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“…We use h 1 to replace h inĝ (t; β, θ). More discussion can be found in Chang, Xue and Zhu (2010) and Pang and Xue (2012).…”

Section: Methodology and Asymptotic Propertiesmentioning

confidence: 96%

Estimation for Partially Linear Single-index Instrumental Variables Models

Zhou

Yang

Han

et al. 2015

Communications in Statistics - Simulation and Computation

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In this paper, we generalize the partially linear single-index models to the scenario with some endogenous covariates variables. It is well known that the estimators of based on the existing methods are often inconsistent because of the endogeneity of covariates. To deal with the endogenous variables, we introduce some auxiliary instrumental variables. A three-stage estimation procedure is proposed for partially linear single-index instrumental variables models. The first stage is to obtain a linear projection of endogenous variables on a set of instrumental variables, the second stage is to estimate the link function by using local linear smoother for given constant parameters, and the last stage is to obtain the estimators of constant parameters based on the estimating equation. Asymptotic normality is established for the proposed estimators. Some simulation studies are undertaken to assess the finite sample performance of the proposed estimation procedure.

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“…Such an assumption assures that the unknown link function are arbitrarily well approximated by spline models. We note that most of the SIMs in the existing literature have been expressed in such a form [17,26,36,37,39,41]. The main task is therefore to approximate each f ℓ with a spline function and to estimate the spline coefficients.…”

Section: Multivariate Single-index Models 211 the Basic Modelmentioning

confidence: 99%

Large-sample estimation and inference in multivariate single-index models

Peng

2019

Journal of Multivariate Analysis

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By optimizing index functions against different outcomes, we propose a multivariate single-index model (SIM) for development of medical indices that simultaneously work with multiple outcomes. Fitting of a multivariate SIM is not fundamentally different from fitting a univariate SIM, as the former can be written as a sum of multiple univariate SIMs with appropriate indicator functions. What have not been carefully studied are the theoretical properties of the parameter estimators. Because of the lack of asymptotic results, no formal inference procedure has been made available for multivariate SIMs. In this paper, we examine the asymptotic properties of the multivariate SIM parameter estimators. We show that, under mild regularity conditions, estimators for the multivariate SIM parameters are indeed √ n-consistent and asymptotically normal. We conduct a simulation study to investigate the finite-sample performance of the corresponding estimation and inference procedures. To illustrate its use in practice, we construct an index measure of urine electrolyte markers for assessing the risk of hypertension in individual subjects.

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Estimation for the single-index models with random effects

Cited by 25 publications

References 38 publications

SIMEX estimation for single-index model with covariate measurement error

SIMEX estimation for single-index model with covariate measurement error

Estimation for Partially Linear Single-index Instrumental Variables Models

Large-sample estimation and inference in multivariate single-index models

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