The paper studies estimation of partially linear hazard regression models with varying coefficients for multivariate survival data. A profile pseudopartiallikelihood estimation method is proposed. The estimation of the parameters of the linear part is accomplished via maximization of the profile pseudopartiallikelihood, whereas the varyingcoefficient functions are considered as nuisance parameters that are profiled out of the likelihood. It is shown that the estimators of the parameters are root n consistent 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 estimators proposed. A real data set is analysed to illustrate the methodology proposed.
Varyingcoefficient linear models arise from multivariate nonparametric regression, nonlinear time series modelling and forecasting, functional data analysis, longitudinal data analysis and others. It has been a common practice to assume that the varying coefficients are functions of a given variable, which is often called an index. To enlarge the modelling capacity substantially, this paper explores a class of varyingcoefficient linear models in which the index is unknown and is estimated as a linear combination of regressors and/or other variables. We search for the index such that the derived varyingcoefficient model provides the least squares approximation to the underlying unknown multidimensional regression function. The search is implemented through a newly proposed hybrid backfitting algorithm. The core of the algorithm is the alternating iteration between estimating the index through a onestep scheme and estimating coefficient functions through onedimensional local linear smoothing. The locally significant variables are selected in terms of a combined use of the tstatistic and the Akaike information criterion. We further extend the algorithm for models with two indices. Simulation shows that the methodology proposed has appreciable flexibility to model complex multivariate nonlinear structure and is practically feasible with average modern computers. The methods are further illustrated through the Canadian mink–muskrat data in 1925–1994 and the pound–dollar exchange rates in 1974–1983.
more » « less NSFPAR ID:
 10405789
 Publisher / Repository:
 Oxford University Press
 Date Published:
 Journal Name:
 Journal of the Royal Statistical Society Series B: Statistical Methodology
 Volume:
 65
 Issue:
 1
 ISSN:
 13697412
 Page Range / eLocation ID:
 p. 5780
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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