Selection of estimators is an essential task in modeling. A general framework is that the estimators of a distribution are obtained by minimizing a function (the estimating function) and assessed using another function (the assessment function). A classical case is that both functions estimate...

In this article, we focus on data arriving sequentially by blocks in a stream. A semiparametric regression model involving a common effective dimension reduction (EDR) direction <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\beta $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">β</mi> </math> </EquationSource> </InlineEquation> is assumed in each block. Our goal is to estimate this direction at each arrival of a new block. A...</equationsource></equationsource></inlineequation>

We consider models based on multivariate counting processes, including multi-state models. These models are specified semi-parametrically by a set of functions and real parameters. We consider inference for these models based on coarsened observations, focusing on families of smooth estimators...