title: A Monte Carlo method for variance estimation for estimators based on induced smoothing.
abstract: An important issue in statistical inference for semiparametric models is how to provide reliable and consistent variance estimation. Brown and Wang (2005. Standard errors and covariance matrices for smoothed rank estimators. Biometrika 92: , 732-746) proposed a variance estimation procedure based on an induced smoothing for non-smooth estimating functions. Herein a Monte Carlo version is developed that does not require any explicit form for the estimating function itself, as long as numerical evaluation can be carried out. A general convergence theory is established, showing that any one-step iteration leads to a consistent variance estimator and continuation of the iterations converges at an exponential rate. The method is demonstrated through the Buckley-James estimator and the weighted log-rank estimators for censored linear regression, and rank estimation for multiple event times data.
authors.affiliation: Department of Biostatistics, Columbia University, New York, NY 10032, USA zj7@columbia.edu.
authors.forename: Zhezhen
authors.initials: Z
authors.lastname: Jin
authors.affiliation: Division of Biostatistics, New York University School of Medicine, New York, NY 10016, USA.
authors.forename: Yongzhao
authors.initials: Y
authors.lastname: Shao
authors.affiliation: Department of Statistics, Columbia University, New York, NY 10027, USA.
authors.forename: Zhiliang
authors.initials: Z
authors.lastname: Ying
mesh_terms: D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D009010:Monte Carlo Method
keywords: Accelerated failure time model; Asymptotic fiducialdistribution; Buckley–James estimator; Censored data; Contraction mapping; Estimating function; Kaplan–Meier estimator; Monte Carlointegration; Rank estimator