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project R-5529

Title : Statistical inference in varying coefficient models with censored data (R-5529)
Abstract: Modeling the relation between a response and explanatory variables is a key activity in statistics. Linear models are convenient but often unsatisfactory in applications. In classical linear models the impact of an explanatory variable on the response is additive and the corresponding regression coefficient (slope) is a constant. Practical applications however need models that allow (unknown) functional coefficients rather than constant coefficients; such models are called varying coefficients models (VCM's). VCM's are a.o. very instrumental in longitudinal, survival and econometric studies. Methodology for VCM's has been developed for complete data. For responses that are subject to right censoring or interval censoring (incomplete data) many methodological questions are open. The aim of this project is to extend the existing methodology for incomplete data through (i) estimation of the functional coefficients and (ii) variable selection in VCM's. The estimation technique uses P-splines (a smoothing technique); variable selection is based on the nonnegative garrote (a powerful subset regression technique). For complete data, the use of P-spline smoothing in combination with variable selection via the nonnegative garrote has been successful in a variety of applications. The aim of this project is to show that also for censored responses, P-spline smoothing combined with nonnegative garrote variable selection provides a sound tool for statistical modeling.
Period of project : 1/10/2014to30/09/2016