Joint Estimation of the Mean and Error Distribution in Generalized Linear Models

Huang, Alan

doi:10.1080/01621459.2013.824892

Cited by 13 publications

(32 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, we focus our attention on the accuracy of the point estimates of β . The results here complement those found in Huang (2013, Section 6).…”

Section: Practical Implicationssupporting

confidence: 90%

“…Although it is not hard to derive a score function for F (e.g. Huang, 2013, Section 3.3), it turns out to be rather difficult to compute the nuisance tangent space explicitly. This is also noted in Jørgensen & Knudsen (2004, Section 6.2).…”

Section: The Orthogonality Of Parametersmentioning

confidence: 99%

“…The idea of jointly estimating the mean and error distribution in GLMs is considered in more detail in Huang (2013). In that paper, it is demonstrated that inferences on β based on profiling out the error distribution F in the likelihood can be more accurate than inferences based on QL methods.…”

Section: Practical Implicationsmentioning

confidence: 99%

“…Recall that the relative root mean-square error of an estimator

\overset{β}{true}

is defined as the root mean-square error of

\overset{β}{true}

divided by the absolute value | β | of the parameter. The simulation settings are based on a leukemia survival dataset from Davison & Hinkley (1997) and a mine injury dataset from Myers et al (2010), and are described in more detail in Sections 6.1 and 6.2 of Huang (2013). The particular semiparametric estimation approach we use for estimating β is based on empirical likelihood and is described in more detail in Section 4 of Huang (2013).…”

Section: Practical Implicationsmentioning

confidence: 99%

See 3 more Smart Citations

Orthogonality of the mean and error distribution in generalized linear models

Huang

Rathouz

2016

Communications in Statistics - Theory and Methods

Self Cite

View full text Add to dashboard Cite

We show that the mean-model parameter is always orthogonal to the error distribution in generalized linear models. Thus, the maximum likelihood estimator of the mean-model parameter will be asymptotically efficient regardless of whether the error distribution is known completely, known up to a finite vector of parameters, or left completely unspecified, in which case the likelihood is taken to be an appropriate semiparametric likelihood. Moreover, the maximum likelihood estimator of the mean-model parameter will be asymptotically independent of the maximum likelihood estimator of the error distribution. This generalizes some well-known results for the special cases of normal, gamma and multinomial regression models, and, perhaps more interestingly, suggests that asymptotically efficient estimation and inferences can always be obtained if the error distribution is nonparametrically estimated along with the mean. In contrast, estimation and inferences using misspecified error distributions or variance functions are generally not efficient.

show abstract

“…Here, we focus our attention on the accuracy of the point estimates of β . The results here complement those found in Huang (2013, Section 6).…”

Section: Practical Implicationssupporting

confidence: 90%

Section: The Orthogonality Of Parametersmentioning

confidence: 99%

Section: Practical Implicationsmentioning

confidence: 99%

“…Recall that the relative root mean-square error of an estimator

\overset{β}{true}

is defined as the root mean-square error of

\overset{β}{true}

Section: Practical Implicationsmentioning

confidence: 99%

See 2 more Smart Citations

Orthogonality of the mean and error distribution in generalized linear models

Huang

Rathouz

2016

Communications in Statistics - Theory and Methods

Self Cite

View full text Add to dashboard Cite

show abstract

“…The DRM (1) may be extended to incorporate a covariate; for instance, Luo & Tsai () introduced covariate Z through the conditional density of X :

italicdF false(x false| Z = z false) = exp {α + false(β^{⊤} z false) x} {dF}_{0} false(x false) .

This formulation is particularly suitable for modelling a nonlinear monotonic relationship between an outcome variable and a covariate. Rathouz & Gao (), Huang & Rathouz (), and Huang () formulated a natural extension of generalized linear models (GLM) in the direction of DRM by further assuming that

normalE false(X false| Z = z false) = η false({boldγ}^{⊤} z false)

for some known link function

η

, where

boldγ

is a parameter vector. In contrast to Luo & Tsai (),

β

in this formulation is implicitly defined as a smooth function of

F_{0} false(x false)

, z , and

boldγ

.…”

Section: Introductionmentioning

confidence: 99%

Empirical likelihood inference for multiple censored samples

Cai

Chen

2017

Can J Statistics

View full text Add to dashboard Cite

We present a semiparametric approach to inference on the underlying distributions of multiple right‐ and/or left‐censored samples with fixed censoring points and focus on effective estimation of population quantiles and distribution functions. We pool information across multiple censored samples through a semiparametric density ratio model and propose an empirical likelihood approach to inference. This approach achieves high efficiency without making restrictive model assumptions. The resultant estimator is asymptotically normal, and the resulting distribution function estimator and quantile estimator are more efficient than estimators obtained from the classic nonparametric methods, such as the empirical distribution and sample quantile. In addition, the proposed approach permits consistent estimation of distribution functions and quantiles on a larger domain than would otherwise be possible using the classic methods. Simulation studies suggest that the proposed method is robust against misspecification of the density ratio function and against outliers. Our approach is further illustrated with an application to the analysis of real lumber strength data. The Canadian Journal of Statistics 46: 212–232; 2018 © 2017 Statistical Society of Canada

show abstract

Estimating linear causality in the presence of latent variables

Fei

Yang

2017

Cluster Comput

View full text Add to dashboard Cite

Joint Estimation of the Mean and Error Distribution in Generalized Linear Models

Cited by 13 publications

References 25 publications

Orthogonality of the mean and error distribution in generalized linear models

Orthogonality of the mean and error distribution in generalized linear models

Empirical likelihood inference for multiple censored samples

Estimating linear causality in the presence of latent variables

Contact Info

Product

Resources

About