Robustness

  • Robust Inference for Location Parameters The focus of our research has been on optimality under a finite set of distributional shapes or challenges. An example is an estimator that minimizes the mean-squared-error under the assumption that the observations are either Cauchy distributed or follow a Gaussian law, that is, an estimator that can simultaneously withstand the challenge posed by the Cauchy and the Gaussian.

  • Robust Inference for Regression Parameters The adaptation of configural polysampling methods to the regression case and in particular the use of contaminated Gaussian challenges have been studied by our group.

  • Robust Inference for Scale Parameters Robustness in the scale case is similar to the estimation of location when the challenges include asymmetric distributional shapes. In both cases, one must agree on a functional to be estimated and one must considered bias along with variance. Risk-minimizing estimators under a variety of distributional challenges can be computed and exhibit interesting behavior.

  • Robust Estimation Estimators minimizing the risk under the assumptions of a heavy-tailed error distribution are typically resistant to outliers, but can at the same time be inefficient if there are no outliers present in the data. Combining efficiency and just-in-time-resistance – i.e. only when really needed – is achieved by minimizing the risk under the assumption of a finite set of distributions, including a heavy-tailed one.

  • Weights of Evidence A weight of evidence is a metric for evaluating possibilities (hypotheses) in the light of observations. Our group has derived weights of evidence that are optimal in a broad sense and provide resistance to outliers conditional on the observations.

  • Kalman Filtering We have studied the use of scrambled net quasi-Monte Carlo methods in the computation of generalized Kalman filters. Robustness and efficiency can be reconciled in models where the innovation-distribution is allowed to be any one of a carefully chosen finite set of possibilities.

  • Robust Variograms We studied the use of highly resistant scale estimators in the estimation of variograms. Since in the estimation of variograms each observation is used several times, the resistance properties of scale estimators, such as breakdown points, do not immediately carry over to the variogram. Influence functions and other robustness indicators for our estimators have been derived and the fitting of parametric variograms has also been studied.

  • Latent Variables and Factor Analysis We have developed a number of methods for analyzing two-way tables. In latent variable models, the rows of such tables are typically time-ordered and the columns refer to linked observed time series. An example is given by the returns for various assets observed over a certain period.