Proportional likelihood ratio models for mean regression

Huang, Alan; Rathouz, Paul J.

doi:10.1093/biomet/asr075

Cited by 21 publications

(12 citation statements)

References 10 publications

(18 reference statements)

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“…In practice, q ( t ) is often prespecified to balance the computational convenience and model flexibility. The choices used in the literature include the Box‐Cox transformation function, the simple linear function q ( t )= t , the so‐called “general” function

q false(t false) = {false(t, normal l o g t, {false[normal l o g false(t false) false]}^{2} false)}^{T}

, and a rich class of functions

q false(t false) = {false(normal l o g t, t^{0.5}, t, t^{1.5}, t^{2} false)}^{T}

. In this paper, we use a two‐dimensional function

q false(t false) = {false(t, t^{2} false)}^{T} .

As will be shown in the following, this q ( t ) function allows fast computation and usually works well for smooth functions through Taylor expansion approximations.…”

Section: Semiparametric Bayesian Approach Via Density Ratio Modelsmentioning

confidence: 99%

Semiparametric Bayesian analysis of accelerated failure time models with cluster structures

Shen

2017

Statistics in Medicine

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In this paper, we develop a Bayesian semiparametric accelerated failure time model for survival data with cluster structures. Our model allows distributional heterogeneity across clusters and accommodates their relationships through a density ratio approach. Moreover, a nonparametric mixture of Dirichlet processes prior is placed on the baseline distribution to yield full distributional flexibility. We illustrate through simulations that our model can greatly improve estimation accuracy by effectively pooling information from multiple clusters, while taking into account the heterogeneity in their random error distributions. We also demonstrate the implementation of our method using analysis of Mayo Clinic Trial in Primary Biliary Cirrhosis.

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q false(t false) = {false(t, normal l o g t, {false[normal l o g false(t false) false]}^{2} false)}^{T}

, and a rich class of functions

q false(t false) = {false(normal l o g t, t^{0.5}, t, t^{1.5}, t^{2} false)}^{T}

. In this paper, we use a two‐dimensional function

q false(t false) = {false(t, t^{2} false)}^{T} .

As will be shown in the following, this q ( t ) function allows fast computation and usually works well for smooth functions through Taylor expansion approximations.…”

Section: Semiparametric Bayesian Approach Via Density Ratio Modelsmentioning

confidence: 99%

Semiparametric Bayesian analysis of accelerated failure time models with cluster structures

Shen

2017

Statistics in Medicine

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“…Interpretations similar to those in Sections can also be obtained for other models such as the Gilbert–Lele–Vardi biased sampling model (Gilbert et al ., ) and the semiparametric single‐index model (Ichimura, ). In this context, note that Rathouz and Gao () and Huang and Rathouz () modelled the mean directly, where the parameter β is essentially a contrast in the mean response.…”

Section: Relationship To Other Modelsmentioning

confidence: 99%

A Minimum Relative Entropy Based Correlation Model Between the Response and Covariates

Bhattacharya

Al-Talib

2016

Journal of the Royal Statistical Society Series B: Statistical Methodology

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A semiparametric model is presented utilizing dependence between a response and several covariates. We show that this model is optimum when the marginal distributions of the response and the covariates are known. This model extends the generalized linear model and the proportional likelihood ratio model when the marginal distributions are unknown. New interpretations of known models such as the logistic regression model, density ratio model and selection bias model are obtained in terms of dependence between variables. For estimation of parameters, a simple algorithm is presented which is guaranteed to converge. It is also the same regardless of the choice of the distribution for response and covariates; hence, it can fit a very wide variety of useful models. Asymptotic properties of the estimators of model parameters are derived. Real data examples are discussed to illustrate our approach and simulation experiments are performed to compare with existing procedures.

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“…Following Tan (2009) and Huang and Rathouz (2012), and with γ = (α, λ) T , we define the auxiliary function…”

Section: A2 Auxiliary Function and Lemmasmentioning

confidence: 99%

Spectral Density Ratio Models for Multivariate Extremes

Carvalho

Davison

2014

Journal of the American Statistical Association

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The modeling of multivariate extremes has received increasing recent attention because of its importance in risk assessment. In classical statistics of extremes, the joint distribution of two or more extremes has a nonparametric form, subject to moment constraints. This paper develops a semiparametric model for the situation where several multivariate extremal distributions are linked through the action of a covariate on an unspecified baseline distribution, through a socalled density ratio model. Theoretical and numerical aspects of empirical likelihood inference for this model are discussed, and an application is given to pairs of extreme forest temperatures.

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Proportional likelihood ratio models for mean regression

Cited by 21 publications

References 10 publications

Semiparametric Bayesian analysis of accelerated failure time models with cluster structures

Semiparametric Bayesian analysis of accelerated failure time models with cluster structures

A Minimum Relative Entropy Based Correlation Model Between the Response and Covariates

Spectral Density Ratio Models for Multivariate Extremes

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