Statistical inference for varying coefficient functions and qualitative constraints (R-5210)

We consider models with varying coefficients, i.e. linear models in which the response and/or explanatory variables vary with another variable, for example time. These types of models can for example be used in HIV research, where the number of T-cells decreases over time and in addition depends on the number of T-cells at the time of infection. Moreover we study ordinary differential equations with varying coefficients that allow describing the dynamics of continuously changing processes and we develop techniques for dealing with data containing measurement errors as well as censoring. The developed methods can be extended to generalized varying coefficient models in order to deal with data that contain categories or the estimation of quantiles. We estimate the varying coefficients by P-splines. This widely used sparse flexible smoothing technique has as an important advantage (over other smoothing techniques such as B-splines or smoothing splines) that the unknown functions can be modeled in a rich basis, while introducing sparsity by adding a penalty. The main aim of this project is to develop statistical methods that focus on qualitative features of the varying coefficients functions, e.g. whether a coefficient is really varying (in contrast to being constant) or whether it is an increasing function. Moreover we want to test general hypotheses concerning the coefficient functions, by exploiting the nice properties of P-splines such as its linearity in the basis functions.

Keywords:MISSING VALUES, MULTIVARIATE CATEGORICAL DATA

Disciplines:Applied mathematics in specific fields, Statistics and numerical methods