This paper develops a method for estimating the spectrum of a stationary process using time series traces recorded from experimental designs. Our procedure estimates the "common" log-spectrum and the variability over the traces (or subjects) using a mixed effects model. We combine the use of spatially adaptive smoothing methods with recursive dyadic partitioning to construct a predictive model. The method is easy to implement and can handle large data sets because is uses the discrete wavelet transform which is computationally efficient. Numerical studies confirm that the proposed method performs very well despite its simplicity. The method is also applied to a multi-subject electroencephalogram data set.

International audienceWe focus on the performances of tree-structured wavelet estimators belonging to a large family of keep-or-kill rules, namely the Vertical Block Thresholding family. For each estimator, we provide the maximal functional space (maxiset) for which the quadratic risk reaches a given rate of convergence. Following a discussion on the maxiset embeddings, we identify the ideal estimator of this family, that is the one associated with the largest maxiset. We emphasize the importance of such a result since the ideal estimator is different from the usual (plug-in) estimator used to mimic the performances of the Oracle. Finally, we confirm the good performances of the ideal estimator compared to the other elements of that family through extensive numerical experiments

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International audienceWe study the maxiset performance of a large collection of block thresholding wavelet estimators, namely the horizontal block thresholding family. We provide sufficient conditions on the choices of rates and threshold values to ensure that the involved adaptive estimators obtain large maxisets. Moreover, we prove that any estimator of such a family reconstructs the Besov balls with a near-minimax optimal rate that can be faster than the one of any separable thresholding estimator. Then, we identify, in particular cases, the best estimator of such a family, that is, the one associated with the largest maxiset. As a particularity of this paper, we propose a refined approach that models method-dependent threshold values. By a series of simulation studies, we confirm the good performance of the best estimator by comparing it with the other members of its family

The extraction of cooccurrences between two events, A and B, is a central learning mechanism shared by all species capable of associative learning. Formally, the cooccurrence of events A and B appearing in a sequence is measured by the transitional probability (TP) between these events, and it corresponds to the probability of the second stimulus given the first (i.e., p(B|A)). In the present study, nonhuman primates (Guinea baboons, Papio papio) were exposed to a serial version of the XOR (i.e., exclusive-OR), in which they had to process sequences of three stimuli: A, B, and C. In this manipulation, first-order TPs (i.e., AB and BC) were uninformative due to their transitional probabilities being equal to .5 (i.e., p(B|A) = p(C|B) = .5), while second-order TPs were fully predictive of the upcoming stimulus (i.e., p(C|AB) = 1). In Experiment 1, we found that baboons were able to learn second-order TPs, while no learning occurred on first-order TPs. In Experiment 2, this pattern of results was replicated, and a final test ruled out an alternative interpretation in terms of proximity to the reward. These results indicate that a nonhuman primate species can learn a nonlinearly separable problem such as the XOR. They also provide fine-grained empirical data to test models of statistical learning on the interaction between the learning of different orders of TPs.