Efficient estimation of a semiparametric partially linear varying coefficient model

Ahmad, Ibrahim A.; Leelahanon, Sittisak; Li, Qi

doi:10.1214/009053604000000931

Cited by 155 publications

(106 citation statements)

References 35 publications

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“…With respect to developments in semiparametric dynamic modelling, various estimation and testing issues have been discussed for the case where data are strictly stationary (such as Gao (2007)) since the publication of Robinson (1988Robinson ( , 1989. Li, Huang, Li and Fu (2002), Zhang, Lee and Song (2002), Ahmad, Leelahanon and Li (2005), and Fan and Huang (2005) studied partially varying coefficient estimation for the conditional mean model. To the best of our knowledge, the semiparametric dynamic quantile modelling like (2) has not been studied in either econometrics or statistics literature.…”

Section: Introductionmentioning

confidence: 99%

Semiparametric quantile regression estimation in dynamic models with partially varying coefficients

Cai

Zhang

2012

Journal of Econometrics

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We study quantile regression estimation for dynamic models with partially varying coefficients so that the values of some coefficients may be functions of informative covariates.Estimation of both parametric and nonparametric functional coefficients are proposed.In particular, we propose a three stage semiparametric procedure. Both consistency and asymptotic normality of the proposed estimators are derived. We demonstrate that the parametric estimators are root-n consistent and the estimation of the functional coefficients is oracle. In addition, efficiency of parameter estimation is discussed and a simple efficient estimator is proposed. A simple and easily implemented test for the hypothesis of varying-coefficient is proposed. A Monte Carlo experiment is conducted to evaluate the performance of the proposed estimators.KEY WORDS: Efficiency; nonlinear time series; partially linear; partially varying coefficients; quantile regression; semiparametric. * We thank two referees and the guest Editors for their very helpful comments and suggestions. We also thank the audiences at the

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Section: Introductionmentioning

confidence: 99%

Semiparametric quantile regression estimation in dynamic models with partially varying coefficients

Cai

Zhang

2012

Journal of Econometrics

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“…The primary advantage of such a model (over a fully semiparametric specification) is its potential for efficiency gains stemming from the additional information about constancy of some of the parameter functions. Such partially linear semiparametric models have been extensively studied for sampling with no spatial or cross-sectional dependence by, e.g., Ahmad, Leelahanon & Li (2005), Kai, Li & Zou (2011) and Cai & Xiao (2012). In the spatial autoregression literature, Su (2012) and Zhang (2013) both focus on the case when ρ (z i ) = ρ 0 over its domain, however, with varying assumptions about x i β (z i ) (in our notation).…”

Section: Special Case: Partially Linear Spatial Autoregressive Modelmentioning

confidence: 99%

Semiparametric estimation and testing of smooth coefficient spatial autoregressive models

Malikov

Sun²

2017

Journal of Econometrics

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This paper considers a flexible semiparametric spatial autoregressive (mixed-regressive) model in which unknown coefficients are permitted to be nonparametric functions of some contextual variables to allow for potential nonlinearities and parameter heterogeneity in the spatial relationship. Unlike other semiparametric spatial dependence models, ours permits the spatial autoregressive parameter to meaningfully vary across units and thus allows the identification of a neighborhood-specific spatial dependence measure conditional on the vector of contextual variables. We propose several (locally) nonparametric GMM estimators for our model. The developed two-stage estimators incorporate both the linear and quadratic orthogonality conditions and are capable of accommodating a variety of data generating processes, including the instance of a pure spatially autoregressive semiparametric model with no relevant regressors as well as multiple partially linear specifications. All proposed estimators are shown to be consistent and asymptotically normal. We also contribute to the literature by putting forward two test statistics to test for parameter constancy in our model. Both tests are consistent.

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“…As a special case, some of the coefficient functions can be constant. This is sometimes called the partially linear varying coefficient model [10]. If a coefficient function is linear in T , then the model includes a main effect for the covariate, and its cross-product interaction with T as commonly used in linear regressions.…”

Section: Varying Coefficient Measurement Error Modelmentioning

confidence: 99%

Varying Coefficients Model with Measurement Error

Greene

2008

Biometrics

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We propose a semi-parametric partially varying coefficient model to study the relationship between serum creatinine concentration and the glomerular filtration rate (GFR) among kidney donors and patients with chronic kidney disease. A regression model is used to relate serum creatinine to GFR and demographic factors in which coefficient of GFR is expressed as a function of age to allow its effect to be age-dependent. GFR measurements obtained from the clearance of a radioactively labeled isotope are assumed to be a surrogate for the true GFR, with the relationship between measured and true GFR expressed using an additive error model. We use local corrected score equations to estimate parameters and coefficient functions, and propose an expected generalized cross-validation (EGCV) method to select the kernel bandwidth. The performance of the proposed methods, which avoid distributional assumptions on the true GFR and residuals, is investigated by simulation. Application of the proposed model to several clinical data sets reveals the presence of a consistent relationship between serum creatinine and true GFR that appears to apply both to healthy kidney donors and to chronic renal disease patients.

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Efficient estimation of a semiparametric partially linear varying coefficient model

Cited by 155 publications

References 35 publications

Semiparametric quantile regression estimation in dynamic models with partially varying coefficients

Semiparametric quantile regression estimation in dynamic models with partially varying coefficients

Semiparametric estimation and testing of smooth coefficient spatial autoregressive models

Varying Coefficients Model with Measurement Error

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