Nonparametric estimation of the mixing density using polynomials

We consider the problem of estimating the mixing density $f$ from $n$ i.i.d. observations distributed according to a mixture density with unknown mixing distribution. In contrast with finite mixtures models, here the distribution of the hidden variable is not bounded to a finite set but is spread out over a given interval. We propose an approach to construct an orthogonal series estimator of the mixing density $f$ involving Legendre polynomials. The construction of the orthonormal sequence varies from one mixture model to another. Minimax upper and lower bounds of the mean integrated squared error are provided which apply in various contexts. In the specific case of exponential mixtures, it is shown that the estimator is adaptive over a collection of specific smoothness classes, more precisely, there exists a constant A\textgreater{}0 such that, when the order $m$ of the projection estimator verifies $m\sim A \log(n)$, the estimator achieves the minimax rate over this collection. Other cases are investigated such as Gamma shape mixtures and scale mixtures of compactly supported densities including Beta mixtures. Finally, a consistent estimator of the support of the mixing density $f$ is provided

Process model based development of disassembly tools

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Disassembly processes require flexible tools for loosening and handling operations. Today, disassembly processes demand a great deal of manual labour and a vast variety of tools. Partly destructive tools which generate and use new acting surfaces are able to increase the economic viability owing to their flexibility and their promotion of the reuse of components. This article describes selected methods of acting surface generation and their application for prototypical tools.DFG, SFB 281, Demontagefabriken zur Rückgewinnung von Ressourcen in Produkt- und Materialkreisläufe

A semiparametric extension of the stochastic block model for longitudinal networks

To model recurrent interaction events in continuous time, an extension of the stochastic block model is proposed where every individual belongs to a latent group and interactions between two individuals follow a conditional inhomogeneous Poisson process with intensity driven by the individuals' latent groups. The model is shown to be identifiable and its estimation is based on a semiparametric variational expectation-maximization algorithm. Two versions of the method are developed, using either a nonparametric histogram approach (with an adaptive choice of the partition size) or kernel intensity estimators. The number of latent groups can be selected by an integrated classification likelihood criterion. Finally, we demonstrate the performance of our procedure on synthetic experiments, analyse two datasets to illustrate the utility of our approach and comment on competing methods

OMP-type Algorithm with Structured Sparsity Patterns for Multipath Radar Signals

A transmitted, unknown radar signal is observed at the receiver through more than one path in additive noise. The aim is to recover the waveform of the intercepted signal and to simultaneously estimate the direction of arrival (DOA). We propose an approach exploiting the parsimonious time-frequency representation of the signal by applying a new OMP-type algorithm for structured sparsity patterns. An important issue is the scalability of the proposed algorithm since high-dimensional models shall be used for radar signals. Monte-Carlo simulations for modulated signals illustrate the good performance of the method even for low signal-to-noise ratios and a gain of 20 dB for the DOA estimation compared to some elementary method

Model-based graph clustering of a collection of networks using an agglomerative algorithm

Graph clustering is the task of partitioning a collection of observed networks into groups of similar networks. Here similarity means networks have a similar structure or graph topology. To this end, a model-based approach is developed, where the networks are modelled by a finite mixture model of stochastic block models. Moreover, a computationally efficient clustering algorithm is developed. The procedure is an agglomerative hierarchical algorithm that maximizes the so-called integrated classification likelihood criterion. The bottom-up algorithm consists of successive merges of clusters of networks. Those merges require a means to match block labels of two stochastic block models to overcome the label-switching problem. This problem is addressed with a new distance measure for the comparison of stochastic block models based on their graphons. The algorithm provides a cluster hierarchy in form of a dendrogram and valuable estimates of all model parameters

Adaptive Density Estimation in the Pile-up Model Involving Measurement Errors

International audienceMotivated by fluorescence lifetime measurements this paper considers the problem of nonparametric density estimation in the pile-up model. Adaptive nonparametric estimators are proposed for the pile-up model in its simple form as well as in the case of additional measurement errors. Furthermore, oracle type risk bounds for the mean integrated squared error (MISE) are provided. Finally, the estimation methods are assessed by a simulation study and the application to real fluorescence lifetime data

Medication adherence following kidney transplantation: a grounded theory study of transplant recipients' perspectives

Background: Medication adherence has shown to be problematic for many renal transplant recipients. While factors promoting or inhibiting medication adherence have been extensively researched, little is known about the processes leading to this behaviour as perceived by kidney transplant recipients. Also, no research on the perspectives of German kidney transplant recipients has yet been carried out. Research Question: The question underpinning this research was: “How do German renal transplant recipients perceive the processes leading to medication adherence or non-adherence?” Methods: Following informed consent, telephone interviews with 17 German renal transplant recipients were conducted, transcribed verbatim, and analysed according to the tenets of constructive Grounded Theory, until theoretical saturation was reached. The research has been approved by the research ethics committees of the School of Healthcare Sciences and the German Society of Nursing Science. Results: This research established the theory of medication-taking as a symbol of living with a chronic condition. This theory is underpinned by two categories: in the category reflecting on one’s own position, the participants discussed their role regarding the intake of medication, which was perceived very ambivalently and as just one component of self-management following transplantation. In the category experiencing facilitators and challenges, participants reported factors supporting or impeding medication-taking. Crucially, these are perceived very individually: what one finds helpful or challenging may be perceived in a fundamentally different way by someone else. Conclusions: This research has similar findings to other research in this field, such as the fact that renal transplantation is not a cure for a chronic condition. However, in contrast to other research, it has found a strong connection between medication-taking and participants’ self-reflection of being chronically ill. In this regard, it has emphasised the need for individualised care, preferably in the form of a team approach that includes patients and families as well as the different healthcare professions