On the Reynaud-Bouret–Rivoirard–Tuleau-Malot problem

By using biorthogonal wavelets, Reynaud-Bouret, Rivoirard and Tuleau-Malot provide the adaptive and optimal [Formula: see text]-risk estimation for density functions (not necessarily having compact support) in a Besov space [Formula: see text] [P. Reynaud-Bouret, V. Rivoirard and C. Tuleau-Malot, Adaptive density estimation: A curse of support?, J. Stat. Plan. Inference 141(1) (2011) 115–139]. The authors pose an open problem: Can [Formula: see text]-risk ([Formula: see text]) estimation be given in their setting? In this paper, we try to solve that problem for [Formula: see text] by using wavelet estimators.

Inferring Team Task Plans from Human Meetings: A Generative Modeling Approach with Logic-Based Prior

We aim to reduce the burden of programming and deploying autonomous systems to work in concert with people in time-critical domains such as military field operations and disaster response. Deployment plans for these operations are frequently negotiated on-the-fly by teams of human planners. A human operator then translates the agreed-upon plan into machine instructions for the robots. We present an algorithm that reduces this translation burden by inferring the final plan from a processed form of the human team's planning conversation. Our hybrid approach combines probabilistic generative modeling with logical plan validation used to compute a highly structured prior over possible plans, enabling us to overcome the challenge of performing inference over a large solution space with only a small amount of noisy data from the team planning session. We validate the algorithm through human subject experimentations and show that it is able to infer a human team's final plan with 86% accuracy on average. We also describe a robot demonstration in which two people plan and execute a first-response collaborative task with a PR2 robot. To the best of our knowledge, this is the first work to integrate a logical planning technique within a generative model to perform plan inference.

A statistical application of the quantile mechanics approach: MTM estimators for the parameters of t and gamma distributions

In this paper, we revisit the quantile mechanics approach, which was introduced by Steinbrecher and Shaw (Steinbrecher, G. & Shaw, W. T. (2008) Quantile mechanics. European. J. Appl. Math.19, 87–112). Our objectives are (i) to derive the method of trimmed moments (MTM) estimators for the parameters of gamma and Student's t distributions, and (ii) to examine their large- and small-sample statistical properties. Since trimmed moments are defined through the quantile function of the distribution, quantile mechanics seems like a natural approach for achieving objective (i). To accomplish the second goal, we rely on the general large sample results for MTMs, which were established by Brazauskas et al. (Brazauskas, V., Jones, B. L. & Zitikis, R. (2009) Robust fitting of claim severity distributions and the method of trimmed moments. J. Stat. Plan. Inference139, 2028–2043), and then use Monte Carlo simulations to investigate small-sample behaviour of the newly derived estimators. We find that, unlike the maximum likelihood method, which usually yields fully efficient but non-robust estimators, the MTM estimators are robust and offer competitive trade-offs between robustness and efficiency. These properties are essential when one employs gamma or Student's t distributions in such outlier-prone areas as insurance and finance.