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This paper presents a multinomial multi-state micro-level reserving model, denoted mCube. We propose a unified framework for modelling the time and the payment process for IBNR and RBNS claims and for modeling IBNR claim counts. We use multinomial distributions for the time process and spliced mixture models for the payment process. We illustrate the excellent performance of the proposed model on a real data set of a major insurance company consisting of bodily injury claims. It is shown that the proposed model produces a best estimate distribution that is centered around the true reserve.

As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which rely on minimal to no model assumptions. These are defined according to an optimization criterion that maximizes a nonparametric measure of association. The original estimators are nonsparse, which means that all variables contribute to the model. However, in many practical applications, an SDR technique may be called for that is sparse and as such, intrinsically performs sufficient variable selection (SVS). This paper examines how such a sparse SDR estimator can be constructed. Three variants are investigated, depending on different measures of association: distance covariance, martingale difference divergence and ball covariance. A simulation study shows that each of these estimators can achieve correct variable selection in highly nonlinear contexts, yet are sensitive to outliers and computationally intensive. The study sheds light on the subtle differences between the methods. Two examples illustrate how these new estimators can be applied in practice, with a slight preference for the option based on martingale difference divergence in the bioinformatics example.

The direpack package aims to establish a set of modern statistical dimension reduction techniques into the Python universe as a single, consistent package. The dimension reduction methods included resort into three categories: projection pursuit based dimension reduction, sufficient dimension reduction, and robust M estimators for dimension reduction. As a corollary, regularized regression estimators based on these reduced dimension spaces are provided as well, ranging from classical principal component regression up to sparse partial robust M regression. The package also contains a set of classical and robust pre-processing utilities, including generalized spatial signs, as well as dedicated plotting functionality and cross-validation utilities. Finally, direpack has been written consistent with the scikit-learn API, such that the estimators can flawlessly be included into (statistical and/or machine) learning pipelines in that framework.