The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform

Jian Huang - One of the best experts on this subject based on the ideXlab platform.

  • a spline based semiparametric maximum likelihood estimation method for the cox model with interval censored data
    Scandinavian Journal of Statistics, 2010
    Co-Authors: Yingying Zhang, Lei Hua, Jian Huang
    Abstract:

    Abstract.  We propose a spline-based semiparametric maximum likelihood approach to analysing the Cox model with interval-censored data. With this approach, the baseline cumulative hazard function is approximated by a monotone B-spline function. We extend the generalized Rosen algorithm to compute the maximum likelihood estimate. We show that the estimator of the Regression Parameter is asymptotically normal and semiparametrically efficient, although the estimator of the baseline cumulative hazard function converges at a rate slower than root-n. We also develop an easy-to-implement method for consistently estimating the standard error of the estimated Regression Parameter, which facilitates the proposed inference procedure for the Cox model with interval-censored data. The proposed method is evaluated by simulation studies regarding its finite sample performance and is illustrated using data from a breast cosmesis study.

  • a spline based semiparametric maximum likelihood estimation method for the cox model with interval censored data
    Scandinavian Journal of Statistics, 2010
    Co-Authors: Yingying Zhang, Jian Huang
    Abstract:

    We propose a spline-based semiparametric maximum likelihood approach to analysing the Cox model with interval-censored data. With this approach, the baseline cumulative hazard function is approximated by a monotone B-spline function. We extend the generalized Rosen algorithm to compute the maximum likelihood estimate. We show that the estimator of the Regression Parameter is asymptotically normal and semiparametrically efficient, although the estimator of the baseline cumulative hazard function converges at a rate slower than root-"n". We also develop an easy-to-implement method for consistently estimating the standard error of the estimated Regression Parameter, which facilitates the proposed inference procedure for the Cox model with interval-censored data. The proposed method is evaluated by simulation studies regarding its finite sample performance and is illustrated using data from a breast cosmesis study. Copyright (c) 2010 Board of the Foundation of the Scandinavian Journal of Statistics.

  • efficient estimation for the proportional hazards model with interval censoring
    Annals of Statistics, 1996
    Co-Authors: Jian Huang
    Abstract:

    The maximum likelihood estimator (MLE) for the proportional hazards model with "case 1" interval censored data is studied. It is shown that the MLE for the Regression Parameter is asymptotically normal with $\sqrt{n}$ convergence rate and achieves the information bound, even though the MLE for the baseline cumulative hazard function only converges at $n^{1/3}$ rate. Estimation of the asymptotic variance matrix for the MLE of the Regression Parameter is also considered. To prove our main results, we also establish a general theorem showing that the MLE of the finite-dimensional Parameter in a class of semiparametric models is asymptotically efficient even though the MLE of the infinite-dimensional Parameter converges at a rate slower than $\sqrt{n}$. The results are illustrated by applying them to a data set from a tumorigenicity study.

Yingying Zhang - One of the best experts on this subject based on the ideXlab platform.

  • a spline based semiparametric maximum likelihood estimation method for the cox model with interval censored data
    Scandinavian Journal of Statistics, 2010
    Co-Authors: Yingying Zhang, Lei Hua, Jian Huang
    Abstract:

    Abstract.  We propose a spline-based semiparametric maximum likelihood approach to analysing the Cox model with interval-censored data. With this approach, the baseline cumulative hazard function is approximated by a monotone B-spline function. We extend the generalized Rosen algorithm to compute the maximum likelihood estimate. We show that the estimator of the Regression Parameter is asymptotically normal and semiparametrically efficient, although the estimator of the baseline cumulative hazard function converges at a rate slower than root-n. We also develop an easy-to-implement method for consistently estimating the standard error of the estimated Regression Parameter, which facilitates the proposed inference procedure for the Cox model with interval-censored data. The proposed method is evaluated by simulation studies regarding its finite sample performance and is illustrated using data from a breast cosmesis study.

  • a spline based semiparametric maximum likelihood estimation method for the cox model with interval censored data
    Scandinavian Journal of Statistics, 2010
    Co-Authors: Yingying Zhang, Jian Huang
    Abstract:

    We propose a spline-based semiparametric maximum likelihood approach to analysing the Cox model with interval-censored data. With this approach, the baseline cumulative hazard function is approximated by a monotone B-spline function. We extend the generalized Rosen algorithm to compute the maximum likelihood estimate. We show that the estimator of the Regression Parameter is asymptotically normal and semiparametrically efficient, although the estimator of the baseline cumulative hazard function converges at a rate slower than root-"n". We also develop an easy-to-implement method for consistently estimating the standard error of the estimated Regression Parameter, which facilitates the proposed inference procedure for the Cox model with interval-censored data. The proposed method is evaluated by simulation studies regarding its finite sample performance and is illustrated using data from a breast cosmesis study. Copyright (c) 2010 Board of the Foundation of the Scandinavian Journal of Statistics.

Tong Zhang - One of the best experts on this subject based on the ideXlab platform.

  • sparse nonlinear Regression Parameter estimation under nonconvexity
    International Conference on Machine Learning, 2016
    Co-Authors: Zhuoran Yang, Zhaoran Wang, Han Liu, Yonina C Eldar, Tong Zhang
    Abstract:

    We study Parameter estimation for sparse nonlinear Regression. More specifically, we assume the data are given by y = f(xτβ*) + e, where f is nonlinear. To recover β*, we propose an l1- regularized least-squares estimator. Unlike classical linear Regression, the corresponding optimization problem is nonconvex because of the nonlinearity of f. In spite of the nonconvexity, we prove that under mild conditions, every stationary point of the objective enjoys an optimal statistical rate of convergence. Detailed numerical results are provided to back up our theory.

  • sparse nonlinear Regression Parameter estimation and asymptotic inference
    arXiv: Machine Learning, 2015
    Co-Authors: Zhuoran Yang, Zhaoran Wang, Yonina C Eldar, Tong Zhang
    Abstract:

    We study Parameter estimation and asymptotic inference for sparse nonlinear Regression. More specifically, we assume the data are given by y = f(x > ) + , where f is nonlinear. To recover , we propose an ‘1-regularized least-squares estimator. Unlike classical linear Regression, the corresponding optimization problem is nonconvex because of the nonlinearity of f. In spite of the nonconvexity, we prove that under mild conditions, every stationary point of the objective enjoys an optimal statistical rate of convergence. In addition, we provide an ecient algorithm that provably converges to a stationary point. We also access the uncertainty of the obtained estimator. Specifically, based on any stationary point of the objective, we construct valid hypothesis tests and confidence intervals for the low dimensional components of the high-dimensional Parameter . Detailed numerical results are provided to back up our theory.

Zhuoran Yang - One of the best experts on this subject based on the ideXlab platform.

  • sparse nonlinear Regression Parameter estimation under nonconvexity
    International Conference on Machine Learning, 2016
    Co-Authors: Zhuoran Yang, Zhaoran Wang, Han Liu, Yonina C Eldar, Tong Zhang
    Abstract:

    We study Parameter estimation for sparse nonlinear Regression. More specifically, we assume the data are given by y = f(xτβ*) + e, where f is nonlinear. To recover β*, we propose an l1- regularized least-squares estimator. Unlike classical linear Regression, the corresponding optimization problem is nonconvex because of the nonlinearity of f. In spite of the nonconvexity, we prove that under mild conditions, every stationary point of the objective enjoys an optimal statistical rate of convergence. Detailed numerical results are provided to back up our theory.

  • sparse nonlinear Regression Parameter estimation and asymptotic inference
    arXiv: Machine Learning, 2015
    Co-Authors: Zhuoran Yang, Zhaoran Wang, Yonina C Eldar, Tong Zhang
    Abstract:

    We study Parameter estimation and asymptotic inference for sparse nonlinear Regression. More specifically, we assume the data are given by y = f(x > ) + , where f is nonlinear. To recover , we propose an ‘1-regularized least-squares estimator. Unlike classical linear Regression, the corresponding optimization problem is nonconvex because of the nonlinearity of f. In spite of the nonconvexity, we prove that under mild conditions, every stationary point of the objective enjoys an optimal statistical rate of convergence. In addition, we provide an ecient algorithm that provably converges to a stationary point. We also access the uncertainty of the obtained estimator. Specifically, based on any stationary point of the objective, we construct valid hypothesis tests and confidence intervals for the low dimensional components of the high-dimensional Parameter . Detailed numerical results are provided to back up our theory.

Lei Hua - One of the best experts on this subject based on the ideXlab platform.

  • a spline based semiparametric maximum likelihood estimation method for the cox model with interval censored data
    Scandinavian Journal of Statistics, 2010
    Co-Authors: Yingying Zhang, Lei Hua, Jian Huang
    Abstract:

    Abstract.  We propose a spline-based semiparametric maximum likelihood approach to analysing the Cox model with interval-censored data. With this approach, the baseline cumulative hazard function is approximated by a monotone B-spline function. We extend the generalized Rosen algorithm to compute the maximum likelihood estimate. We show that the estimator of the Regression Parameter is asymptotically normal and semiparametrically efficient, although the estimator of the baseline cumulative hazard function converges at a rate slower than root-n. We also develop an easy-to-implement method for consistently estimating the standard error of the estimated Regression Parameter, which facilitates the proposed inference procedure for the Cox model with interval-censored data. The proposed method is evaluated by simulation studies regarding its finite sample performance and is illustrated using data from a breast cosmesis study.