Quasi-likelihood Estimation in Semiparametric Models

Severini, Thomas A.; Staniswalis, Joan G.

doi:10.2307/2290852

Cited by 126 publications

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“…confounders) are nuisance parameters. Efficient estimation for partially linear models has been extensively studied and well understood for independent data; see, for example, Chen (1988),Speckman (1988) and Severini & Staniswalis (1994). Martinussen et al.…”

Section: Introductionmentioning

confidence: 99%

Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines

Huang¹,

Zhang²,

Zhou³

2007

Scandinavian J Statistics

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We consider marginal semiparametric partially linear models for longitudinal/clustered data and propose an estimation procedure based on a spline approximation of the non-parametric part of the model and an extension of the parametric marginal generalized estimating equations (GEE). Our estimates of both parametric part and non-parametric part of the model have properties parallel to those of parametric GEE, that is, the estimates are efficient if the covariance structure is correctly specified and they are still consistent and asymptotically normal even if the covariance structure is misspecified. By showing that our estimate achieves the semiparametric information bound, we actually establish the efficiency of estimating the parametric part of the model in a stronger sense than what is typically considered for GEE. The semiparametric efficiency of our estimate is obtained by assuming only conditional moment restrictions instead of the strict multivariate Gaussian error assumption. Copyright 2007 Board of the Foundation of the Scandinavian Journal of Statistics..

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Section: Introductionmentioning

confidence: 99%

Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines

Huang¹,

Zhang²,

Zhou³

2007

Scandinavian J Statistics

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“…The basic model is that, for a known function μ (·) and a true but unknown function θ 0 ( z ), where, given , has mean 0 and covariance matrix Σ( τ 0 ) for a parameter τ 0 . Note that the function θ 0 (·) is evaluated repeatedly, and thus this problem is very much different from the standard partially linear model (Severini and Staniswalis, 1994). This problem has a large literature, with many kernel‐based methods (Zeger and Diggle (1994), Hoover et al.…”

Section: Introductionmentioning

confidence: 99%

Semiparametric Estimation in General Repeated Measures Problems

Lin

Carroll

2005

Journal of the Royal Statistical Society Series B: Statistical Methodology

103

132

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Summary. The paper considers a wide class of semiparametric problems with a parametric part for some covariate effects and repeated evaluations of a nonparametric function. Special cases in our approach include marginal models for longitudinal or clustered data, conditional logistic regression for matched case-control studies, multivariate measurement error models, generalized linear mixed models with a semiparametric component, and many others. We propose profile kernel and backfitting estimation methods for these problems, derive their asymptotic distributions and show that in likelihood problems the methods are semiparametric efficient. Although generally not true, it transpires that with our methods profiling and backfitting are asymptotically equivalent. We also consider pseudolikelihood methods where some nuisance parameters are estimated from a different algorithm. The methods proposed are evaluated by using simulation studies and applied to the Kenya haemoglobin data.

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“…We remark that a similar non‐parametric function in a generalised linear model context was studied by Severini & Staniswalis () and Lin & Carroll () using the so‐called GEE (generalised estimating equation) approach, which has, however, several drawbacks as discussed by Sutradhar, Warriyar & Zheng () for count data.…”

Section: Estimationmentioning

confidence: 82%

“…Note that the unconditional mean μ ij ( β , θ , σ τ , ψ (·)) can be computed in practice using the approach

μ_{ij} false(bold-italicβ, θ, σ_{τ}, ψ (\cdot) false) ≃ \frac{1}{N} {false\sum}_{w = 1}^{N} μ_{ij}^{*} false(bold-italicβ, θ, σ_{τ}, ψ (\cdot) false| τ_{italiciw} false),

where N is a large number such as N = 1000, and τ iw , w = 1, …, N , is a random sample from a standard normal distribution. Notice that the recursive nature of formula implies that the unconditional mean μ ij ( β , θ , σ τ , ψ (·)) in or depends not only on the present covariate values ( x ij , z ij ), but also on the past covariate values from ( x i , j −1 , z i , j −1 ) to ( x i 1 , z i 1 ), which is a major difference between the SBDML model and the semi‐parametric fixed models studied by other authors such as Severini & Staniswalis (), and Lin & Carroll ().…”

Section: Proposed Sbdml Modelmentioning

confidence: 99%

Generalised quasi‐likelihood inference in a semi‐parametric binary dynamic mixed logit model

Zheng

Sutradhar

2018

Aus NZ J of Statistics

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There exists a recent study where dynamic mixed-effects regression models for count data have been extended to a semi-parametric context. However, when one deals with other discrete data such as binary responses, the results based on count data models are not directly applicable. In this paper, we therefore begin with existing binary dynamic mixed models and generalise them to the semi-parametric context. For inference, we use a new semi-parametric conditional quasi-likelihood (SCQL) approach for the estimation of the non-parametric function involved in the semi-parametric model, and a semi-parametric generalised quasilikelihood (SGQL) approach for the estimation of the main regression, dynamic dependence and random effects variance parameters. A semi-parametric maximum likelihood (SML) approach is also used as a comparison to the SGQL approach. The properties of the estimators are examined both asymptotically and empirically. More specifically, the consistency of the estimators is established and finite sample performances of the estimators are examined through an intensive simulation study.

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Quasi-likelihood Estimation in Semiparametric Models

Cited by 126 publications

References 0 publications

Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines

Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines

Semiparametric Estimation in General Repeated Measures Problems

Generalised quasi‐likelihood inference in a semi‐parametric binary dynamic mixed logit model

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