Tutorials
The tutorials will take place during the conference, and in parallel with the invited, organized and contributed sessions.
Heuristic methods for Model Selection and Estimation
Dietmar Maringer, University of Basel
Model selection and estimation involve optimization to find the ideal solution. More often than not, there is no closedform solution, and one has to rely on numerical procedures. The underlying optimization problems, however, are rarely wellbehaved: the search spaces can be discontinuous, have multiple optima, or pose massive combinatorial problems. This undermines the quality of traditional numerical search and optimization techniques of the kind usually used for optimization problems in statistical and econometric software. Numerical procedures typically consist of many iterations, each of which includes a "creation step" in which one or more new candidate solutions are created, and an "acceptance step" where a decision is made whether the new candidate is replacing the previous solution or not.
Traditional methods put all their efforts into the creation step: exploiting the (assumed) properties of the search space and construction an improvement based on the characteristics of the current candidate(s). An actual improvement is then accepted, while failure of finding an improved new solution in one step results in stopping, assuming that the actual optimum has been found. These methods hinge on the creation step: if underlying assumptions about the search space are violated, then they can stop prematurely, or the creation can be misguided and never find the solution.
New methods therefore put more emphasis on the acceptance step and relax the construction phase. Typically, nondeterministic elements are added to the guided construction or even replace them, while the acceptance step enforces a preference for improvements, but also facilitates overcoming local optima. Many of these "heuristic methods" draw inspiration from nature; prominent members of this group are evolutionary methods such as genetic algorithms or differential evolution. Although they usually require more iterations than traditional methods, they still can be faster than some traditional methods as the creation step is often much faster, and they are substantially faster than simple Monte Carlo methods. They can tackle much more demanding search problems (i.e., are suitable for more sophisticated statistical and econometric models), and, best of all, they can often be shown to converge to the global optimum.
This tutorial presents some of the more popular heuristic methods and demonstrates how they can be used for model selection and estimation, including applications to time series analysis, multivariate data analysis, and robust statistics.
Robust Estimation, Inference and Prediction
Stefan Van Aelst, KU Leuven
Statistical models are at best a good approximation of the often complex process that generated the available data. Moreover, individual observations may deviate from the process that produces the majority of the data due to rare events, technological failures and so on. To address these issues when analyzing the data robust methods need to be used that still yield reliable results for the majority of the observations while some fraction of the data deviates from the statistical model. The robust methods then allow to detect the deviating observations for further inspection or may guide adjustments to the model to obtain a better approximation of reality. However, not all outlying observations are meaningful and in that case the model should not be adjusted to accommodate the outliers, but the inference should still be reliable in the presence of these outliers.
In this tutorial we will start with an overview of robust methods to estimate the model parameters in regression and multivariate locationscale models. Both methods for lowdimensional and highdimensional data will be discussed and the challenges encountered for both types of data are highlighted. Moreover, we then focus on methods for robust model selection, hypothesis testing and robust prediction models. Robust and computationally efficient resampling techniques will be discussed in this context.
