Single index regression models in the presence of censoring depending on the covariates

Consider a random vector (X',Y)', where X is d-dimensional and Y is one-dimensional.We assume that Y is subject to random right censoring. The aim of this paper is twofold. First, we propose a new estimator of the joint distribution of (X',Y)'. This estimator overcomes the common curse-of-dimensionality problem, by using a new dimension reduction technique. Second, we assume that the relation between X and Y is given by a mean regression single index model, and propose a new estimator of the parameters in this model. The asymptotic properties of all proposed estimators are obtained.

[1]  Thomas M. Stoker,et al.  Investigating Smooth Multiple Regression by the Method of Average Derivatives , 2015 .

[2]  D. Mason,et al.  Erratum to: A general result on the uniform in bandwidth consistency of kernel-type function estimators , 2015 .

[3]  O. Lopez.  Nonparametric Estimation of the Multivariate Distribution Function in a Censored Regression Model with Applications , 2011 .

[4]  Olivier Lopez,et al.  Single-index Regression models with right-censored responses , 2008, 0803.1112.

[5]  O. Lopez.  Réduction de dimension en présence de données censurées , 2007 .

[6]  Xuewen Lu,et al.  Randomly censored partially linear single-index models , 2007 .

[7]  Shuyuan He,et al.  Asymptotics for a censored generalized linear model with unknown link function , 2007 .

[8]  Cédric Heuchenne,et al.  Polynomial Regression with Censored Data based on Preliminary Nonparametric Estimation , 2007 .

[9]  O. Lopez.  On the Estimation of the Joint Distribution in Regression Models with Censored Responses , 2007 .

[10]  M. Hristache,et al.  On Semiparametric estimation in Single-Index Regression , 2006 .

[11]  Uniform Representation of Product‐Limit Integrals with Applications , 2005 .

[12]  SOME CONVERGENCE THEORY FOR ITERATIVE ESTIMATION PROCEDURES WITH AN APPLICATION TO SEMIPARAMETRIC ESTIMATION , 2005, Econometric Theory.

[13]  Xuewen Lu,et al.  Censored multiple regression by the method of average derivatives , 2005 .

[14]  A. Juditsky,et al.  Direct estimation of the index coefficient in a single-index model , 2001 .

[15]  Jane-Ling Wang,et al.  Dimension reduction for censored regression data , 1999 .

[16]  Michael G. Akritas,et al.  Transfer of tail information in censored regression models , 1999 .

[17]  The least squares method in heteroscedastic censored regression models , 1999 .

[18]  J. Horowitz,et al.  Semiparametric Estimation of a Censored Regression Model with an Unknown Transformation of the Dependent Variable , 1999 .

[19]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[20]  Winfried Stute,et al.  Distributional Convergence under Random Censorship when Covariables are Present , 1996 .

[21]  W. Härdle,et al.  Direct Semiparametric Estimation of Single-Index Models with Discrete Covariates dpsfb950075.ps.tar = Enno MAMMEN J.S. MARRON: Mass Recentered Kernel Smoothers , 1996 .

[22]  M. Akritas.  Nearest Neighbor Estimation of a Bivariate Distribution Under Random Censoring , 1994 .

[23]  Robert P. Sherman,et al.  Maximal Inequalities for Degenerate $U$-Processes with Applications to Optimization Estimators , 1994 .

[24]  Jianqing Fan,et al.  Censored Regression - Local Linear-approximations and Their Applications , 1994 .

[25]  M. Talagrand.  Sharper Bounds for Gaussian and Empirical Processes , 1994 .

[26]  H. Ichimura,et al.  SEMIPARAMETRIC LEAST SQUARES (SLS) AND WEIGHTED SLS ESTIMATION OF SINGLE-INDEX MODELS , 1993 .

[27]  Winfried Stute,et al.  Consistent estimation under random censorship when covariables are present , 1993 .

[28]  W. Härdle,et al.  Optimal Smoothing in Single-index Models , 1993 .

[29]  R. Spady,et al.  AN EFFICIENT SEMIPARAMETRIC ESTIMATOR FOR BINARY RESPONSE MODELS , 1993 .

[30]  Thomas M. Stoker,et al.  Semiparametric Estimation of Index Coefficients , 1989 .

[31]  D. Pollard,et al.  Simulation and the Asymptotics of Optimization Estimators , 1989 .

[32]  D. Pollard,et al.  $U$-Processes: Rates of Convergence , 1987 .

[33]  R. Prentice,et al.  Commentary on Andersen and Gill's "Cox's Regression Model for Counting Processes: A Large Sample Study" , 1982 .