Empirical Likelihood Semiparametric Regression Analysis for Longitudinal Data

Xue, Liugen; Zhu, Lixing

doi:10.1093/biomet/asm066

Cited by 110 publications

(47 citation statements)

References 31 publications

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“…The findings basically agree with that which was discovered by the local linear fitting method of Fan and Li [7] and Xue and Zhu [24]. …”

Section: A Real Examplesupporting

confidence: 90%

“…Similar to Xue and Zhu [24], we can show that if we substitute Condition C1 in Theorem 3.1, with N h 2 / log N → ∞ and N h 5 → 0, that is, if undersmoothing is adopted, then the biased term b(t 0 ) vanished asymptotically. Denote that…”

Section: )And (35)supporting

confidence: 61%

“…In a manner similar to Xue and Zhu [24], we can adjust the weighted residualsη i {g(t 0 )} and then obtain an adjusted empirical likelihood ratio without undersmoothing. Introduce the auxiliary random vectorŝ…”

Section: )And (35)mentioning

confidence: 99%

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Generalized Empirical Likelihood Inference in Partially Linear Errors-in-Variables Models with Longitudinal data

Liu

Xue

Tian

2016

HJMS

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This article is concerned with estimations for longitudinal partial linear models with covariate that is measured with error. We propose a generalized empirical likelihood method by combining correction attenuation and quadratic inference functions. The method takes into account the within-subject correlation without involving direct estimation of nuisance parameters in the correlation matrix. We define a generalized empirical likelihood-based statistic for the regression coefficients and residual adjusted empirical likelihood for the baseline function.The empirical log-likelihood ratios are proven to be asymptotically chi-squared, and the corresponding confidence regions are then constructed. Compared with methods based on normal approximations, the generalized empirical likelihood does not require consistent estimators for the asymptotic variance and bias. Furthermore, a simulation study is conducted to evaluate the performance of the proposed method.

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“…The findings basically agree with that which was discovered by the local linear fitting method of Fan and Li [7] and Xue and Zhu [24]. …”

Section: A Real Examplesupporting

confidence: 90%

Section: )And (35)supporting

confidence: 61%

See 1 more Smart Citation

Generalized Empirical Likelihood Inference in Partially Linear Errors-in-Variables Models with Longitudinal data

Liu

Xue

Tian

2016

HJMS

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“…Xue and Zhu (2007b) derived that an asymptotic presentation of the profile empirical loglikelihood ratiol{θ(t 0 )} asl…”

Section: Mean-corrected Empirical Likelihoodmentioning

confidence: 99%

Empirical likelihood in some nonparametric and semiparametric models

Xue

Zhu

2012

Statistics and Its Interface

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In this very selective overview, we summarise the recent developments by our own and other, on the empirical likelihood in some nonparametric and semiparametric regression models. The models include the partially linear model, the single-index model, the partially linear singleindex model, the varying coefficient model, and so on. The focus of this overview is to expatiate the adjustment and "bias correction" methodologies when Wilks' phenomenon does not hold. The adjustment or bias correction can make the limiting distributions tractable such that they can be directly used to construct the confidence regions of parameters of interest without the assistance of Monte Carlo approximation.

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“…Recently, Shi and Lau (2000) [11], Wang and Jing (2003) [12] considered the partial linear models. Xue and Zhu (2007) [13], Li and Xue (2008) [14] investigated the empirical likelihood confidence regions for a partially linear models with longitudinal data. Other related papers contain Cui and Chen (2003) [15], You et al (2006) [16], Xue and Zhu (2008) [17] and Lu (2009) [18].…”

Section: Introductionmentioning

confidence: 99%

Block Empirical Likelihood for Partially Inear Errors-in-Variables Models With Longitudinal Data

Xia¹,

Da²

2013

Int. J. of Pure and Appl. Math.

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In this paper, block empirical likelihood inference for partially linear errors-in-variables models with longitudinal data are investigated. We apply the block empirical likelihood procedure to accommodate the withingroup correlation of the longitudinal data. The block empirical log-likelihood ratio statistic for the parametric components, which are of primary interest, is suggested. And the nonparametric version of the Wilk's theorem is derived under mild conditions. Thus, the empirical likelihood confidence region with asymptotically correct coverage probabilities for parametric components can be constructed. Simulations are carried out to access the performance of the proposed approach.

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Empirical Likelihood Semiparametric Regression Analysis for Longitudinal Data

Cited by 110 publications

References 31 publications

Generalized Empirical Likelihood Inference in Partially Linear Errors-in-Variables Models with Longitudinal data

Generalized Empirical Likelihood Inference in Partially Linear Errors-in-Variables Models with Longitudinal data

Empirical likelihood in some nonparametric and semiparametric models

Block Empirical Likelihood for Partially Inear Errors-in-Variables Models With Longitudinal Data

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