The main goal of the special interest group is to develop and promote new methods and techniques for analyzing data, in fields like: Optimization techniques, Statistical methods and inference, Neural Networks and Data-mining.
Special Interest Group: “Mathematical Statistics in Optimization” aims at bringing together people from both Engineering and Statistical areas.
Nonparametric regression is a very popular tool for data analysis (e.g., independent observations, censored observations, dependent observations, etc.) because these techniques impose few assumptions about the shape of the mean function. Hence, they are extremely flexible tools for uncovering nonlinear relationships between variables. While nonparametric techniques appear to be feasible and flexible, there are problems:
- The so-called curse of dimensionality (Devroye & Györfi, 1985; Györfi et al.,2002). Recent studies in the literature (Ruppert et al., 2003; Gao, 2007) show that combining parametric and nonparametric approaches (semi-parametric methods and models) may be applied to solve dimensionality reduction problems arising from using fully nonparametric models and methods. Up till now their large sample properties are investigated by means of simulations.
- Most efficient learning algorithms require the tuning of some extra tuning parameters. For practical use, it is often preferable to have a data-driven method to select these parameters even when the i.i.d. assumption is violated (Opsomer et al., 2001; De Brabanter et al., 2011)
- Confidence intervals play a central inferential role in distribution free function estimation (Fan & Gijbels, 1996; Krivobokova et al., 2010; De Brabanter et al., 2011). However, providing a confidence interval with the right coverage is a challenging problem. This is especially the case when the underlying function has a wide range of unknown degrees of smoothness. The confidence interval problem is challenging mainly because it is difficult to directly measure the bias of the function estimate.
- Some quite fundamental problems occur when regression techniques are attempted in the presence of outliers. In case of nonparametric regression the L2 risk is commonly used. However, the L2 norm is extremely sensitive to outliers. A popular method to study robustness properties of estimators are influence functions (Hampel et al., 1986) and maxbias curves (Croux & Haesbrouck, 2001).
The main focus of the special interest group: “Mathematical Statistics in Optimization” is to study asymptotic properties of linear smoothers (asymptotic normality, consistency, etc.), develop variable selection methods and model selection methods for different types of data, investigate robustness properties of developed methods and apply the former in static and/or dynamic regression problems.
Links with Working Groups: WG2 and WG3
Coordinator: De Brabanter Jos & De Brabanter Kris
Members: De Brabanter Jos, De Brabanter Kris, Gijbels Irene, Logist Filip, Gins Geert, Claeskens Gerda, Croux Christophe, Veraverbeke Noel
