3,417 research outputs found
Maximum likelihood estimate for nonparametric signal in white noise by optimal control
The paper is devoted to questions of constructing the maximum likelihood estimate for a nonparametric signal in white noise by considering corresponding problems of optimal control. For signals with bounded derivatives, sensitivity theorems are proved. The theorems state a stability of the maximum likelihood estimate with respect to changing output data. They make possible to reduce the original problem to a standard problem of optimal control which is solved by iterative procedure. For signals of Sobolev type the maximum likelihood estimate is obtained to within a parameter which can be found from a transcendental equation
Stability and convergence in discrete convex monotone dynamical systems
We study the stable behaviour of discrete dynamical systems where the map is
convex and monotone with respect to the standard positive cone. The notion of
tangential stability for fixed points and periodic points is introduced, which
is weaker than Lyapunov stability. Among others we show that the set of
tangentially stable fixed points is isomorphic to a convex inf-semilattice, and
a criterion is given for the existence of a unique tangentially stable fixed
point. We also show that periods of tangentially stable periodic points are
orders of permutations on letters, where is the dimension of the
underlying space, and a sufficient condition for global convergence to periodic
orbits is presented.Comment: 36 pages, 1 fugur
Ex-nihilo: Obstacles Surrounding Teaching the Standard Model
The model of the Big Bang is an integral part of the national curriculum for
England. Previous work (e.g. Baxter 1989) has shown that pupils often come into
education with many and varied prior misconceptions emanating from both
internal and external sources. Whilst virtually all of these misconceptions can
be remedied, there will remain (by its very nature) the obstacle of ex-nihilo,
as characterised by the question `how do you get something from nothing?' There
are two origins of this obstacle: conceptual (i.e. knowledge-based) and
cultural (e.g. deeply held religious viewpoints). The article shows how the
citizenship section of the national curriculum, coming `online' in England from
September 2002, presents a new opportunity for exploiting these.Comment: 6 pages. Accepted for publication in Physics E
Intergenerational justice of what: welfare, resources or capabilities?
An important aspect of intergenerational justice concerns the specification of a 'currency of advantage' that can be used to evaluate distributive outcomes across time. Environmental theorists have introduced several innovative currencies of justice in recent years, such as ecological space and critical natural capital. However they have often downplayed the application of established currencies (such as welfare, resources or capabilities) to issues of futurity. After exploring the merits of a number of rival currencies, it is argued that the currency of 'capabilities to function' provides a promising basis for a theory of justice that takes seriously the rights and duties of intergenerational justice
Educating for Autonomy: Liberalism and Autonomy in the Capabilities Approach
Martha Nussbaum grounds her version of the capabilities approach in political liberalism. In this paper, we argue that the capabilities approach, insofar as it genuinely values the things that persons can actually do and be, must be grounded in a hybrid account of liberalism: in order to show respect for adults, its justification must be political; in order to show respect for children, however, its implementation must include a commitment to comprehensive autonomy, one that ensures that children develop the skills necessary to make meaningful choices about whether or not to exercise their basic capabilities. Importantly, in order to show respect for parents who do not necessarily recognize autonomy as a value, we argue that the liberal state, via its system of public education, should take on the role of ensuring that all children within the state develop a sufficient degree of autonomy
Normal Cones and Thompson Metric
The aim of this paper is to study the basic properties of the Thompson metric
in the general case of a real linear space ordered by a cone . We
show that has monotonicity properties which make it compatible with the
linear structure. We also prove several convexity properties of and some
results concerning the topology of , including a brief study of the
-convergence of monotone sequences. It is shown most of the results are
true without any assumption of an Archimedean-type property for . One
considers various completeness properties and one studies the relations between
them. Since is defined in the context of a generic ordered linear space,
with no need of an underlying topological structure, one expects to express its
completeness in terms of properties of the ordering, with respect to the linear
structure. This is done in this paper and, to the best of our knowledge, this
has not been done yet. The Thompson metric and order-unit (semi)norms
are strongly related and share important properties, as both are
defined in terms of the ordered linear structure. Although and
are only topological (and not metrical) equivalent on , we
prove that the completeness is a common feature. One proves the completeness of
the Thompson metric on a sequentially complete normal cone in a locally convex
space. At the end of the paper, it is shown that, in the case of a Banach
space, the normality of the cone is also necessary for the completeness of the
Thompson metric.Comment: 36 page
Autoregression approximation of a nonparametric diffusion model
We consider a model of small diffusion type where the function which governs the drift term varies in a nonparametric set. We investigate discrete versions of this continuous model with respect to statistical equivalence, in the sense of the asymptotic theory of experiments. It is shown that an Euler difference scheme as a discrete version of the stochastic differential equation is asymptotically equivalent in the sense of Le Cam's deficiency distance, when the discretization step decreases with the noise intensity â. We thus obtain a nonparametric version of diffusion limit results for autoregression. It follows that in the continuous diffusion model, discrete sampling on a uniform grid is asymptotically sufficient. The key technical step utilizes the notion of Hellinger process from semimartingale theory
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