Efficient Sieve Maximum Likelihood Estimation of Time-Transformation Models
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Time transformation models assume the survival time to be linearly related to covariates through an unknown monotonic transformation function and an error term with known distribution. In this article, the sieve method of maximum likelihood is used to estimate the unknown monotonic transformation of survival time. More specifically, a suitable class of Bernstein polynomials is used to estimate the transformation function while preserving monotonicity and smoothness. The proposed estimation method is less parametrically intensive than current time transformation methods. Furthermore, the method produces a smooth estimate of the time transformation, and hence the survival function. We discuss the selection of the number of parameters for the polynomial asymptotically, and for moderate sample sizes. The asymptotic properties of the estimators are shown, including the asymptotic normality and efficiency of the regression coefficient. Simulation studies illustrate that our estimator has good empirical properties in practical sample sizes. The method is demonstrated on two data sets and compared to previous similar works.
KeywordsCensoring Sieve maximum likelihood Semiparametric efficiency Survival analysis Transformation models
AMS Classification62N01 62E20 62P99
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