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A catalytic prior distribution is designed to stabilize a high-dimensional “working model” by shrinking it toward a “simplified model.” The shrinkage is achieved by supplementing the observed data with a small amount of “synthetic data” generated from a predictive distribution under the simpler model. We apply this framework to generalized linear models, where we propose various strategies for the specification of a tuning parameter governing the degree of shrinkage and study resultant theoretical properties. In simulations, the resulting posterior estimation using such a catalytic prior outperforms maximum likelihood estimation from the working model and is generally comparable with or superior to existing competitive methods in terms of frequentist prediction accuracy of point estimation and coverage accuracy of interval estimation. The catalytic priors have simple interpretations and are easy to formulate. [ABSTRACT FROM AUTHOR]

This article is partially a review and partially a contribution. The classical two approaches to robustness, Huber’s minimax and Hampel’s based on influence functions, are reviewed with the accent on distribution classes of a non-neighborhood nature. Mainly, attention is paid to the minimax Huber’s M-estimates of location designed for the classes with bounded quantiles and Meshalkin-Shurygin’s stable M-estimates. The contribution is focused on the comparative performance evaluation study of these estimates, together with the classical robust M-estimates under the normal, double-exponential (Laplace), Cauchy, and contaminated normal (Tukey gross error) distributions. The obtained results are as follows: (i) under the normal, double-exponential, Cauchy, and heavily-contaminated normal distributions, the proposed robust minimax M-estimates outperform the classical Huber’s and Hampel’s M-estimates in asymptotic efficiency; (ii) in the case of heavy-tailed double-exponential and Cauchy distributions, the Meshalkin-Shurygin’s radical stable M-estimate also outperforms the classical robust M-estimates; (iii) for moderately contaminated normal, the classical robust estimates slightly outperform the proposed minimax M-estimates. Several directions of future works are enlisted.

This paper proposes and experimentally validates a two-stage approach for coupled lateral vehicle state and tire model estimation. In a first stage, an extended Kalman filter is employed which provides vehicle slip angles and lateral tire forces from commercial low-cost vehicle sensors. The obtained estimates are exploited in the second stage, where a (quasi-static) tire model is fitted to this data. A major issue in this estimation process is the typical instability of these estimators for situations with (prolonged) straight driving. This issue is traced back to a lack of local observability. The use of a variable model covariance is introduced as a practical method to obtain a stable estimator, irrespective of the unobservability. The developed methodology has a low computational load and the Kalman estimator is able to run in real time, whereas the tire model parameter fitting is cheap enough to run online. The proposed methodology is validated experimentally and provides reliable results in variable driving conditions. [ABSTRACT FROM PUBLISHER]

This article is partially a review and partially a contribution. The classical two approaches to robustness, Huber's minimax and Hampel's based on influence functions, are reviewed with the accent on distribution classes of a non-neighborhood nature. Mainly, attention is paid to the minimax Huber's M-estimates of location designed for the classes with bounded quantiles and Meshalkin-Shurygin's stable M-estimates. The contribution is focused on the comparative performance evaluation study of these estimates, together with the classical robust M-estimates under the normal, double-exponential (Laplace), Cauchy, and contaminated normal (Tukey gross error) distributions. The obtained results are as follows: (i) under the normal, double-exponential, Cauchy, and heavily-contaminated normal distributions, the proposed robust minimax M-estimates outperform the classical Huber's and Hampel's M-estimates in asymptotic efficiency; (ii) in the case of heavy-tailed double-exponential and Cauchy distributions, the Meshalkin-Shurygin's radical stable M-estimate also outperforms the classical robust M-estimates; (iii) for moderately contaminated normal, the classical robust estimates slightly outperform the proposed minimax M-estimates. Several directions of future works are enlisted. [ABSTRACT FROM AUTHOR]

A catalytic prior distribution is designed to stabilize a high-dimensional "working model" by shrinking it toward a "simplified model." The shrinkage is achieved by supplementing the observed data with a small amount of "synthetic data" generated from a predictive distribution under the simpler model. We apply this framework to generalized linear models, where we propose various strategies for the specification of a tuning parameter governing the degree of shrinkage and study resultant theoretical properties. In simulations, the resulting posterior estimation using such a catalytic prior outperforms maximum likelihood estimation from the working model and is generally comparable with or superior to existing competitive methods in terms of frequentist prediction accuracy of point estimation and coverage accuracy of interval estimation. The catalytic priors have simple interpretations and are easy to formulate., Competing Interests: The authors declare no competing interest., (Copyright © 2020 the Author(s). Published by PNAS.)