Dynamic movement primitives (DMP) are motion building blocks suitable for real-world tasks. We suggest a methodology for learning the manifold of task and DMP parameters, which facilitates runtime adaptation to changes in task requirements while ensuring predictable and robust performance. For efficient learning, the parameter space is analyzed using principal component analysis and locally linear embedding. Two manifold learning methods: kernel estimation and deep neural networks, are investigated for a ball throwing task in simulation and in a physical environment. Low runtime estimation errors are obtained for both learning methods, with an advantage to kernel estimation when data sets are small.

In a multiple testing context, we consider a semiparametric mixture model with two components where one component is known and corresponds to the distribution of p-values under the null hypothesis and the other component f is nonparametric and stands for the distribution under the alternative hypothesis. Motivated by the issue of local false discovery rate estimation, we focus here on the estimation of the nonparametric unknown component f in the mixture, relying on a preliminary estimator of the unknown proportion θ of true null hypotheses. We propose and study the asymptotic properties of two different estimators for this unknown component. The first estimator is a randomly weighted kernel estimator. We establish an upper bound for its pointwise quadratic risk, exhibiting the classical nonparametric rate of convergence over a class of Hölder densities. To our knowledge, this is the first result establishing convergence as well as corresponding rate for the estimation of the unknown component in this nonparametric mixture. The second estimator is a maximum smoothed likelihood estimator. It is computed through an iterative algorithm, for which we establish a descent property. In addition, these estimators are used in a multiple testing procedure in order to estimate the local false discovery rate. Their respective performances are then compared on synthetic data.

We consider the high order moments estimator of the frontier of a random pair, introduced by [S. Girard, A. Guillou and G. Stupfler, J. Multivariate Anal. 116 (2013) 172–189]. In the present paper, we show that this estimator is strongly uniformly consistent on compact sets and its rate of convergence is given when the conditional cumulative distribution function belongs to the Hall class of distribution functions.

This paper considers cross-validation as an objective and risk-based method for selecting the smoothing parameter in a non-parametric graduation. In addition, the relative merits of two kernel estimators are compared in the context of mortality graduation. Finally, it is well known in the statistical literature that the use of theoretically superior kernels is not as important as the choice of bandwidth. Our results support this conclusion, suggesting that the focus on such weights is misguided in the actuarial textbooks on moving weighted averages.