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

Towards a Proof Theory of G\"odel Modal Logics

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish completeness and complexity results for these fragments

Quantum mechanics and elements of reality inferred from joint measurements

The Einstein-Podolsky-Rosen argument on quantum mechanics incompleteness is formulated in terms of elements of reality inferred from joint (as opposed to alternative) measurements, in two examples involving entangled states of three spin-1/2 particles. The same states allow us to obtain proofs of the incompatibility between quantum mechanics and elements of reality.Comment: LaTeX, 12 page

Comparing the strength of diagonally non-recursive functions in the absence of Sigma^0_2 induction

We prove that the statement “there is a k such that for every f there is a k-bounded diagonally nonrecursive function relative to f” does not imply weak König’s lemma over . This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that every k-bounded diagonally nonrecursive function computes a 2-bounded diagonally nonrecursive function may fail in the absence of

Resolving flow around tandem cylinders with RANS-LES hybrid methods

The financial support for this project was partly provided by the SGS22/148/OHK2/3T/12

Concept Discovery and Argument Bundles in the Experience Web

In this paper we focus on a particular interesting web user-generated content: people¿s experiences. We extend our previous work on aspect extraction and sentiment analysis and propose a novel approach to create a vocabulary of basic level concepts with the appropriate granularity to characterize a set of products. This concept vocabulary is created by analyzing the usage of the aspects over a set of reviews, and allows us to find those features with a clear positive and negative polarity to create the bundles of arguments. The argument bundles allow us to define a concept-wise satisfaction degree of a user query over a set of bundles using the notion of fuzzy implication, allowing the reuse experiences of other people to the needs a specific user. © Springer International Publishing AG 2016.This research has been partially supported by NASAID (CSIC Intramural 201550E022).Peer Reviewe

Robust Estimators in Generalized Pareto Models

This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calculation of the regulatory capital required by Basel II for a bank to cover operational risk. In this context the tail behavior of the underlying distribution is crucial. This is where extreme value theory enters, suggesting to estimate these high quantiles parameterically using, e.g. GPDs. Robust statistics in this context offers procedures bounding the influence of single observations, so provides reliable inference in the presence of moderate deviations from the distributional model assumptions, respectively from the mechanisms underlying the PBHT.Comment: 26pages, 6 figure

The stubborn non-probabilist : "negation incoherence" and a new way to block the Dutch Book argument

We rigorously specify the class of nonprobabilistic agents which are, we argue, immune to the classical Dutch Book argument. We also discuss the notion of expected value used in the argument as well as sketch future research connecting our results to those concerning incoherence measures

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

The Relationship Between Belief and Credence

Sometimes epistemologists theorize about belief, a tripartite attitude on which one can believe, withhold belief, or disbelieve a proposition. In other cases, epistemologists theorize about credence, a fine-grained attitude that represents one’s subjective probability or confidence level toward a proposition. How do these two attitudes relate to each other? This article explores the relationship between belief and credence in two categories: descriptive and normative. It then explains the broader significance of the belief-credence connection and concludes with general lessons from the debate thus far