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22
V.: Structure adaptive approach for dimension reduction
 Ann. Stat
, 2001
"... We propose a new method of effective dimension reduction for a multiindex model which is based on iterative improvement of the family of average derivative estimates. The procedure is computationally straightforward and does not require any prior information about the structure of the underlying mod ..."
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Cited by 37 (4 self)
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We propose a new method of effective dimension reduction for a multiindex model which is based on iterative improvement of the family of average derivative estimates. The procedure is computationally straightforward and does not require any prior information about the structure of the underlying model. We show that in the case when the effective dimension m of the index space does not exceed 3, this space can be estimated with the rate n −1/2 under rather mild assumptions on the model.
Local Maximum Likelihood Estimation and Inference
 J. Royal Statist. Soc. B
, 1998
"... Local maximum likelihood estimation is a nonparametric counterpart of the widelyused parametric maximum likelihood technique. It extends the scope of the parametric maximum likelihood method to a much wider class of parametric spaces. Associated with this nonparametric estimation scheme is the issu ..."
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Cited by 31 (4 self)
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Local maximum likelihood estimation is a nonparametric counterpart of the widelyused parametric maximum likelihood technique. It extends the scope of the parametric maximum likelihood method to a much wider class of parametric spaces. Associated with this nonparametric estimation scheme is the issue of bandwidth selection and bias and variance assessment. This article provides a unified approach to selecting a bandwidth and constructing con dence intervals in local maximum likelihood estimation. The approach is then applied to leastsquares nonparametric regression and to nonparametric logistic regression. Our experiences in these two settings show that the general idea outlined here is powerful and encouraging.
A Local Likelihood Proportional Hazards Model for Interval Censored Data
, 2000
"... this paper, we focus on the use of local likelihood to smooth the baseline hazard in a proportional hazards regression model. That is, we fit model (1) with a fully parameterized "global" covariate function and a locally parameterized baseline hazard function, (t) . Similar ideas are discu ..."
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Cited by 7 (1 self)
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this paper, we focus on the use of local likelihood to smooth the baseline hazard in a proportional hazards regression model. That is, we fit model (1) with a fully parameterized "global" covariate function and a locally parameterized baseline hazard function, (t) . Similar ideas are discussed by Wu and Tuma
A Partial Likelihood Approach to the Smooth Estimation of Dynamic Covariate Effects
, 2005
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LOCAL PARTIALLIKELIHOOD ESTIMATION FOR LIFETIME DATA
, 2006
"... This paper considers a proportional hazards model, which allows one to examine the extent to which covariates interact nonlinearly with an exposure variable, for analysis of lifetime data. A local partiallikelihood technique is proposed to estimate nonlinear interactions. Asymptotic normality of th ..."
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Cited by 6 (2 self)
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This paper considers a proportional hazards model, which allows one to examine the extent to which covariates interact nonlinearly with an exposure variable, for analysis of lifetime data. A local partiallikelihood technique is proposed to estimate nonlinear interactions. Asymptotic normality of the proposed estimator is established. The baseline hazard function, the bias and the variance of the local likelihood estimator are consistently estimated. In addition, a onestep local partiallikelihood estimator is presented to facilitate the computation of the proposed procedure and is demonstrated to be as efficient as the fully iterated local partiallikelihood estimator. Furthermore, a penalized local likelihood estimator is proposed to select important risk variables in the model. Numerical examples are used to illustrate the effectiveness of the proposed procedures. 1. Introduction. One
PENALIZED VARIABLE SELECTION PROCEDURE FOR COX MODELS WITH SEMIPARAMETRIC RELATIVE RISK
"... We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to simultaneously estimate the parameters and select variables ..."
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Cited by 5 (2 self)
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We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to simultaneously estimate the parameters and select variables for both the parametric and the nonparametric parts. Two penalties are applied sequentially. The first penalty, governing the smoothness of the multivariate nonlinear covariate effect function, provides a smoothing spline ANOVA framework that is exploited to derive an empirical model selection tool for the nonparametric part. The second penalty, either the smoothlyclippedabsolutedeviation (SCAD) penalty or the adaptive LASSO penalty, achieves variable selection in the parametric part. We show that the resulting estimator of the parametric part possesses the oracle property, and that the estimator of the nonparametric part achieves the optimal rate of convergence. The proposed procedures are shown to work well in simulation experiments, and then applied to a real data example on sexually transmitted diseases.
Partially linear hazard regression with varyingcoefficients for multivariate survival data
, 2005
"... Summary. This paper studies estimation of partially linear hazard regression models with varying coefficients for multivariate survival data. A profile pseudopartial likelihood estimation method is proposed. The estimation of the parameters of the linear part is accomplished via maximization of the ..."
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Cited by 4 (2 self)
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Summary. This paper studies estimation of partially linear hazard regression models with varying coefficients for multivariate survival data. A profile pseudopartial likelihood estimation method is proposed. The estimation of the parameters of the linear part is accomplished via maximization of the profile pseudopartial likelihood, while the varyingcoefficient functions are considered as nuisance parameters profiled out of the likelihood. It is shown that the estimators of the parameters are √ nconsistent and the estimators of the nonparametric coefficient functions achieve optimal convergence rates. Asymptotic normality is obtained for the estimators of the finite parameters and varyingcoefficient functions. Consistent estimators of the asymptotic variances are derived and empirically tested, which facilitate inference for the model. We prove that the varyingcoefficient functions can be estimated as well as if the parametric components were known and the failure times within each subject were independent. Simulations are conducted to demonstrate the performance of the proposed estimators. A real dataset is analysed to illustrate the proposed methodology.
Local partial likelihood estimation in proportional hazards regression
 Annals of Statistics
, 2007
"... the estimation of the risk function ψ(x) in the proportional hazards model. Their proposed estimator is based on integrating the estimated derivative function obtained through a local version of the partial likelihood. They proved the large sample properties of the derivative function, but the large ..."
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Cited by 3 (0 self)
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the estimation of the risk function ψ(x) in the proportional hazards model. Their proposed estimator is based on integrating the estimated derivative function obtained through a local version of the partial likelihood. They proved the large sample properties of the derivative function, but the large sample properties of the estimator for the risk function itself were not established. In this paper, we consider direct estimation of the relative risk function ψ(x2) − ψ(x1) for any location normalization point x1. The main novelty in our approach is that we select observations in shrinking neighborhoods of both x1 and x2 when constructing a local version of the partial likelihood, whereas Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661–1690] only concentrated on a single neighborhood, resulting in the cancellation of the risk function in the local likelihood function. The asymptotic properties of our estimator are rigorously established and the variance of the estimator is easily estimated. The idea behind our approach is extended to estimate the differences between groups. A simulation study is carried out. 1. Introduction. The Cox
HAZARD MODELS WITH VARYING COEFFICIENTS FOR MULTIVARIATE FAILURE TIME DATA 1
"... Statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis. A local pseudopartial likelihood procedure is proposed for estimating the unknown coefficient functions. A weighted average estim ..."
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Cited by 2 (0 self)
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Statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis. A local pseudopartial likelihood procedure is proposed for estimating the unknown coefficient functions. A weighted average estimator is also proposed in an attempt to improve the efficiency of the estimator. The consistency and asymptotic normality of the proposed estimators are established and standard error formulas for the estimated coefficients are derived and empirically tested. To reduce the computational burden of the maximum local pseudopartial likelihood estimator, a simple and useful onestep estimator is proposed. Statistical properties of the onestep estimator are established and simulation studies are conducted to compare the performance of the onestep estimator to that of the maximum local pseudopartial likelihood estimator. The results show that the onestep estimator can save computational cost without compromising performance both asymptotically and empirically and that an optimal weighted average estimator is more efficient than the maximum local pseudopartial likelihood estimator. A data set from the Busselton Population Health Surveys is analyzed to illustrate our proposed methodology. 1. Introduction. Multivariate
Nonparametric Models in Binary Choice Fixed Effects Panel Data
"... In this paper we extend the fixed effects approach to deal with endogeneity arising from persistent unobserved heterogeneity to nonlinear panel data with nonparametric components. Specifically, we propose a nonparametric procedure that generalizes Chamberlain’s (1984) conditional logit approach. We ..."
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Cited by 1 (0 self)
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In this paper we extend the fixed effects approach to deal with endogeneity arising from persistent unobserved heterogeneity to nonlinear panel data with nonparametric components. Specifically, we propose a nonparametric procedure that generalizes Chamberlain’s (1984) conditional logit approach. We develop an estimator based on nonlinear stochastic integral equations and provide the asymptotic property of the estimator and an iterative algorithm to implement the estimator. We analyze the small sample behavior of the estimator through a Monte Carlo study, and consider the decision to retire as an illustrative application. JEL Classification: C14; C23