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Pavel Cizek, Tilburg Print
Thursday, 29 November 2012, 12:15 - 13:15

Pavel Cizek, Tilburg University

Robust regression quantiles in censored regression

Abstract: Quantile regression has been extensively studied both in the linear and many nonlinear regression models; the focus here is on the linear regression without and with censoring. One of traditional ways to limit the sensitivity of quantile regression to outliers in the explanatory variables is the downweighting of distant observations. This works to some extent in linear models with a small number of uniformly-distributed or fixed-design covariates, but the weighted quantile regression can still be substantially biased by outliers, especially as the number of covariates increases. On the other hand, globally robust estimators of regression quantiles exhibit complicated or unknown asymptotic behavior even in linear models, which makes their applications or extensions to models with non-iid error structure such as censored regression models highly non-trivial. To facilitate robust estimation in linear models without and with censoring, a new globally robust weighted quantile regression method is first proposed and studied, and later, it is combined with the two-step and three-step estimation procedures of censored regression models

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