arXiv subjects

Peter Ruckdeschel

Publications and source records attributed to Peter Ruckdeschel.

22 records · Page 2Linked to original sources

arXiv2010

Fisher Information in Group-Type Models

In proofs of L_2-differentiability, Lebesgue densities of a central distribution are often assumed right from the beginning. Generalizing Theorem 4.2 of Huber[81], we show that in the class of smooth parametric group models these densities are in fact consequences of a finite Fisher information of the model, provided a suitable representation of the latter is used. The proof uses the notions of absolute continuity in k dimensions and weak differentiability. As examples to which this theorem applies, we spell out a number of models including a correlation model and the general multivariate location and scale model. As a consequence of this approach, we show that in the (multivariate) location scale model, finiteness of Fisher information as defined here is in fact equivalent to L_2-differentiability and to a log-likelihood expansion giving local asymptotic normality of the model. Paralleling Huber's proofs for existence and uniqueness of a minimizer of Fisher information to our situation, we get existence of a minimizer in any weakly closed set of central distributions F. If, additionally to analogue assumptions to those of Huber[81], a certain identifiability condition for the transformation holds, we obtain uniqueness of the minimizer. This identifiability condition is satisfied in the multivariate location scale model.

math.ST↗

arXiv2010

Optimally Robust Kalman Filtering at Work: AO-, IO-, and Simultaneously IO- and AO- Robust Filters

We take up optimality results for robust Kalman filtering from Ruckdeschel[2001,2010] where robustness is understood in a distributional sense, i.e.; we enlarge the distribution assumptions made in the ideal model by suitable neighborhoods, allowing for outliers which in our context may be system-endogenous/propagating or -exogenous/non-propagating, inducing the somewhat conflicting goals of tracking and attenuation. Correspondingly, the cited references provide optimally-robust procedures to deal with each type of outliers separately, but in case of IO-robustness does not say much about the implementation. We discuss this in more detail in this paper. Most importantly, we define a hybrid filter combining AO- and IO-optimal ones, which is able to treat both types of outliers simultaneously, albeit with a certain delay. We check our filters at a reference state space model, and compare the results with those obtained by the ACM filter Martin and Masreliez[1977], Martin[1979] and non-parametric, repeated-median based filters Fried et al.[2006,2007].

stat.CO↗

arXiv2010

Optimally (Distributional-)Robust Kalman Filtering

We present optimality results for robust Kalman filtering where robustness is understood in a distributional sense, i.e.; we enlarge the distribution assumptions made in the ideal model by suitable neighborhoods. This allows for outliers which in our context may be system-endogenous or -exogenous, which induces the somewhat conflicting goals of tracking and attenuation. The corresponding minimax MSE-problems are solved for both types of outliers separately, resulting in closed-form saddle-points which consist of an optimally-robust procedure and a corresponding least favorable outlier situation. The results are valid in a surprisingly general setup of state space models, which is not limited to a Euclidean or time-discrete framework. The solution however involves computation of conditional means in the ideal model, which may pose computational problems. In the particular situation that the ideal conditional mean is linear in the observation innovation, we come up with a straight-forward Huberization, the rLS filter, which is very easy to compute. For this linearity we obtain an again surprising characterization.

math.ST↗

arXiv2009

Infinitesimally Robust Estimation in General Smoothly Parametrized Models

We describe the shrinking neighborhood approach of Robust Statistics, which applies to general smoothly parametrized models, especially, exponential families. Equal generality is achieved by object oriented implementation of the optimally robust estimators. We evaluate the estimates on real datasets from literature by means of our R packages ROptEst and RobLox.

stat.ME↗