Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters

Li, Gaorong; Lin, Lu; Zhu, Lixing

doi:10.1016/j.jmva.2011.08.010

Cited by 58 publications

(16 citation statements)

References 30 publications

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“…For example, Kolaczyk [15] and Chen and Cui [16] made an extension to the generalized linear models. As for other studies, see Baggerly [17], DiCiccio et al [18], Chen and Qin [19], Qin and Lawless [20], Zhu and Xue [21], and Li et al [22] among others. Owen [23] is one of the best references for this field.…”

Section: Introductionmentioning

confidence: 72%

“…,3 ) has a multivariate normal distribution with mean zero, marginal variance 1, and an AR(1) correlation matrix with autocorrelation coefficient 0.7. The binary response vector for each cluster has mean specified by (22) and an AR(1) correlation structure with an autocorrelation coefficient = 0.7. Table 1 reports the simulation results for the average coverage probabilities and the average lengths of the confidence intervals for 1 , 2 , and 3 when the nominal level is 0.95 and the true correlation structure is AR(1) structure.…”

Section: Asymptotic Propertiesmentioning

confidence: 99%

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The Empirical Cressie-Read Test Statistics for Longitudinal Generalized Linear Models

Zhang

Tian

Yang

et al. 2014

Journal of Applied Mathematics

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For the marginal longitudinal generalized linear models (GLMs), we develop the empirical Cressie-Read (ECR) test statistic approach which has been proposed for the independent identically distributed (i.i.d.) case. The ECR test statistic includes empirical likelihood as a special case. By adopting this ECR test statistic approach and taking into account the within-subject correlation, the efficiency theory results of estimation and testing based on ECR are established under some regularity conditions. Although a working correlation matrix is assumed, there is no need to estimate the nuisance parameters in the working correlation matrix based on the quadratic inference function (QIF). Therefore, the proposed ECR test statistic is asymptotically a standard 2 limit under the null hypothesis. It is shown that the proposed method is more efficient even when the working correlation matrix is misspecified. We also evaluate the finite sample performance of the proposed methods via simulation studies and a real data analysis.

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Section: Introductionmentioning

confidence: 72%

Section: Asymptotic Propertiesmentioning

confidence: 99%

The Empirical Cressie-Read Test Statistics for Longitudinal Generalized Linear Models

Zhang

Tian

Yang

et al. 2014

Journal of Applied Mathematics

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“…When dimensionality p of the parameters tends to innity as the sample size n → ∞, this generalized varying-coecient partially linear model was considered by Lam and Fan [7]. More relevant works on the varying-coecient partially linear model can be found in Huang and Zhang [6], Li et al [8] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Calibration of the empirical likelihood for semiparametric varying-coefficient partially linear models with diverging number of parameters

He¹,

Chen²

2018

HJMS

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This article is concerned with the calibration of the empirical likelihood for semiparametric varying-coecient partially linear models with diverging number of parameters. However, there is always substantial lack-of-t, when the empirical likelihood ratio is calibrated by a bias-corrected empirical likelihood, producing tests with type I errors much larger than nominal levels. So we consider an eective calibration method and study the asymptotic behavior of this bias-corrected empirical likelihood ratio function. Some simulation studies are conducted to illustrate our approach.

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“…A lot of research work on variable selection and estimation for the GVCPLM has already been done such as Lam and Fan (2008) [12], Li and Liang (2008) [14], Lu (2008) [21], and Hu and Cui (2010) [5]. When the link function g is identity then the GCVPLM can be simplified into the semiparametric partially linear varying coefficient model (Li et al 2002 [13]; Xia, Zhang and Tong 2004 [29]; Ahmad, Leelahanon and Li 2005 [1]; Kai, Li and Zou 2011 [11]; Li, Lin and Zhu 2012 [16]).…”

Section: Introductionmentioning

confidence: 99%

Identification and Estimation for Generalized Varying Coefficient Partially Linear Models

Wang¹,

Wang²,

Amin³

2016

HJMS

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The generalized varying coefficient partially linear model (GVCPLM) enjoys the flexibility of the generalized varying coefficient model and the parsimony and interpretability of the generalized linear model. Statistical inference of GVCPLM is restricted with a condition that the components of varying and constant coefficients are known in advance. Alternatively, the current study is focused on the structure's identification of varying and constant coefficient for GVCPLM and it is based on the spline basis approximation and the group SCAD. This is proved that the proposed method can consistently determine the structure of the GVCPLM under certain conditions, which means that it can accurately choose the varying and constant coefficients precisely. Simulation studies and a real data application are conducted to assess the infinite sample performance of the proposed method.

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Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters

Cited by 58 publications

References 30 publications

The Empirical Cressie-Read Test Statistics for Longitudinal Generalized Linear Models

The Empirical Cressie-Read Test Statistics for Longitudinal Generalized Linear Models

Calibration of the empirical likelihood for semiparametric varying-coefficient partially linear models with diverging number of parameters

Identification and Estimation for Generalized Varying Coefficient Partially Linear Models

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