Minimax Estimation of Nonregular Parameters and Discontinuity in Minimax Risk

When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic minimax estimation theory for a parameter that is a nondifferentiable transform of a regular parameter, where the nondifferentiable transform is a composite map of a continuous piecewise linear map with a single kink point and a translation-scale equivariant map. The contribution of this paper is two fold. First, this paper extends the local asymptotic minimax theory to nondifferentiable transforms that are a composite map of a Lipschitz continuous map having a finite set of nondifferentiability points and a translation-scale equivariant map. Second, this paper investigates the discontinuity of the local asymptotic minimax risk in the true probability and shows that the proposed estimator remains to be optimal even when the risk is locally robustified not only over the scores at the true probability, but also over the true probability itself. However, the local robustification does not resolve the issue of discontinuity in the local asymptotic minimax risk

The singular continuous diffraction measure of the Thue-Morse chain

The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the Thue-Morse chain, in its realisation as a binary sequence with values in $\{\pm 1\}$. We revisit this example and derive a functional equation together with an explicit form of the corresponding singular continuous diffraction measure, which is related to the known representation as a Riesz product.Comment: 6 pages, 1 figure; revised and improved versio

Data-driven efficient score tests for deconvolution problems

We consider testing statistical hypotheses about densities of signals in deconvolution models. A new approach to this problem is proposed. We constructed score tests for the deconvolution with the known noise density and efficient score tests for the case of unknown density. The tests are incorporated with model selection rules to choose reasonable model dimensions automatically by the data. Consistency of the tests is proved

Orphan medicine incentives: how to address the unmet needs of rare disease patients by optimizing the European orphan medicinal product landscape guiding principles and policy proposals by the European Expert Group for Orphan Drug Incentives (OD expert group)

Today policy makers face the challenge to devise a policy framework that improves orphan medicinal product (OMP) development by creating incentives to deliver treatments where there are none and to authorize innovative and transformative treatments where treatments already exist. The European Expert Group on Orphan Drug Incentives (hereafter, OD Expert Group) came together in 2020 to develop policy proposals to facilitate EU policy makers to meet this challenge. The group brings together representatives of the broad rare disease community, including researchers, academia, patient representatives, members of the investor community, rare disease companies and trade associations. The group's work builds on the recognition that only an ambitious policy agenda developed in a multi-stakeholder setting can bring about the quantum leap needed to address unmet needs of rare disease patients today. Along the OMP development path, the OD Expert Group has identified four main needs that a policy revision should address: 1) Need to improve the R&D ecosystem for basic research and company take-up of development. 2) Need to improve the system of financial incentives and rewards. 3) Need to improve the flexibility, predictability and speed of the regulatory pathway. 4) Need to improve the coherence and predictability of demand and pricing for OMPs. This article presents the results of the OD Expert Group work as a set of guiding principles that the revision of the policy framework should follow and a set of 14 policy proposals that address the main needs of OMP development in Europe today.Functional Genomics of Muscle, Nerve and Brain Disorder

An objective based classification of aggregation techniques for wireless sensor networks

Wireless Sensor Networks have gained immense popularity in recent years due to their ever increasing capabilities and wide range of critical applications. A huge body of research efforts has been dedicated to find ways to utilize limited resources of these sensor nodes in an efficient manner. One of the common ways to minimize energy consumption has been aggregation of input data. We note that every aggregation technique has an improvement objective to achieve with respect to the output it produces. Each technique is designed to achieve some target e.g. reduce data size, minimize transmission energy, enhance accuracy etc. This paper presents a comprehensive survey of aggregation techniques that can be used in distributed manner to improve lifetime and energy conservation of wireless sensor networks. Main contribution of this work is proposal of a novel classification of such techniques based on the type of improvement they offer when applied to WSNs. Due to the existence of a myriad of definitions of aggregation, we first review the meaning of term aggregation that can be applied to WSN. The concept is then associated with the proposed classes. Each class of techniques is divided into a number of subclasses and a brief literature review of related work in WSN for each of these is also presented

Antioxidant Capacity and fatty acid profile of Swinglea glutinosa (BLANCO) MERR, cultivated in Cuba

editorial reviewedThe small tropical tree Swinglea glutinosa (Blanco) Merr. is a member of the Rutaceae family. Originally brought to South America from Southeast Asia, it is used as an ornamental plant in Cuba and as a natural barrier in rural areas and gardens. Extracts from this tree have been assessed for cytotoxic and antimalarial activity in previous studies but never been evaluated its antioxidant activity. Material and Methods: The antioxidant capacity of the methanolic extracts and the fatty acid composition of leaves and fruits S. glutinosa (Blanco) Merr was investigated. Six different chemical methods were used to determine the antioxidant capacity. The fatty acid composition was analyzed using gas chromatography. Results: The IC50 value of the extracts was determined being 28.2 g/mL to leaf extract and 10 μg/mL to fruit extract (in the DPPH method. The concentration of the extracts resulted in increased in the ferric reducing antioxidant power to both extracts tested. The amount of total phenolic content was detected as 48.5 mg and 35.9 gallic acid equivalent (GAE)/g in the fruit and the leaf extract, respectively; meanwhile the total antioxidant capacity was 94.93 and 75.3 mg ascorbic acid equivalent (AE)/g for fruits and leaves, respectively. The peroxidation lipid assays (FTC and TBA methods) shows highest antioxidant effect for the leaf extract. Conclusions: The results permit to deduce that the fruit extract has highest anti-radical effect and the leaf extract has highest effect against the lipid peroxidation. The major fatty acid in the composition of Swinglea glutinosa was found to be the ω6 (linoleic) and ω9 (oleic) acids by GC analysis, with 0.5 % for both. This study reveals that Swinglea glutinosa is an attractive source of ω fatty acid components, especially the essential ones, as well as of effective natural antioxidants

Detecting the direction of a signal on high-dimensional spheres: Non-null and Le Cam optimality results

We consider one of the most important problems in directional statistics, namely the problem of testing the null hypothesis that the spike direction $\theta$ of a Fisher-von Mises-Langevin distribution on the $p$-dimensional unit hypersphere is equal to a given direction $\theta_0$. After a reduction through invariance arguments, we derive local asymptotic normality (LAN) results in a general high-dimensional framework where the dimension $p_n$ goes to infinity at an arbitrary rate with the sample size $n$, and where the concentration $\kappa_n$ behaves in a completely free way with $n$, which offers a spectrum of problems ranging from arbitrarily easy to arbitrarily challenging ones. We identify various asymptotic regimes, depending on the convergence/divergence properties of $(\kappa_n)$, that yield different contiguity rates and different limiting experiments. In each regime, we derive Le Cam optimal tests under specified $\kappa_n$ and we compute, from the Le Cam third lemma, asymptotic powers of the classical Watson test under contiguous alternatives. We further establish LAN results with respect to both spike direction and concentration, which allows us to discuss optimality also under unspecified $\kappa_n$. To investigate the non-null behavior of the Watson test outside the parametric framework above, we derive its local asymptotic powers through martingale CLTs in the broader, semiparametric, model of rotationally symmetric distributions. A Monte Carlo study shows that the finite-sample behaviors of the various tests remarkably agree with our asymptotic results.Comment: 47 pages, 4 figure

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

Asymptotic equivalence of discretely observed diffusion processes and their Euler scheme: small variance case

This paper establishes the global asymptotic equivalence, in the sense of the Le Cam $\Delta$-distance, between scalar diffusion models with unknown drift function and small variance on the one side, and nonparametric autoregressive models on the other side. The time horizon $T$ is kept fixed and both the cases of discrete and continuous observation of the path are treated. We allow non constant diffusion coefficient, bounded but possibly tending to zero. The asymptotic equivalences are established by constructing explicit equivalence mappings.Comment: 21 page