3,195 research outputs found
A note on quadratic forms of stationary functional time series under mild conditions
We study distributional properties of a quadratic form of a stationary
functional time series under mild moment conditions. As an important
application, we obtain consistency rates of estimators of spectral density
operators and prove joint weak convergence to a vector of complex Gaussian
random operators. Weak convergence is established based on an approximation of
the form via transforms of Hilbert-valued martingale difference sequences. As a
side-result, the distributional properties of the long-run covariance operator
are established
Locally Stationary Functional Time Series
The literature on time series of functional data has focused on processes of
which the probabilistic law is either constant over time or constant up to its
second-order structure. Especially for long stretches of data it is desirable
to be able to weaken this assumption. This paper introduces a framework that
will enable meaningful statistical inference of functional data of which the
dynamics change over time. We put forward the concept of local stationarity in
the functional setting and establish a class of processes that have a
functional time-varying spectral representation. Subsequently, we derive
conditions that allow for fundamental results from nonstationary multivariate
time series to carry over to the function space. In particular, time-varying
functional ARMA processes are investigated and shown to be functional locally
stationary according to the proposed definition. As a side-result, we establish
a Cram\'er representation for an important class of weakly stationary
functional processes. Important in our context is the notion of a time-varying
spectral density operator of which the properties are studied and uniqueness is
derived. Finally, we provide a consistent nonparametric estimator of this
operator and show it is asymptotically Gaussian using a weaker tightness
criterion than what is usually deemed necessary
A note on Herglotz's theorem for time series on function spaces
In this article, we prove Herglotz's theorem for Hilbert-valued time series.
This requires the notion of an operator-valued measure, which we shall make
precise for our setting. Herglotz's theorem for functional time series allows
to generalize existing results that are central to frequency domain analysis on
the function space. In particular, we use this result to prove the existence of
a functional Cram{\'e}r representation of a large class of processes, including
those with jumps in the spectral distribution and long-memory processes. We
furthermore obtain an optimal finite dimensional reduction of the time series
under weaker assumptions than available in the literature. The results of this
paper therefore enable Fourier analysis for processes of which the spectral
density operator does not necessarily exist
OUTCOME OF ADOPTIONS: HAVE COUPLES REALISED THEIR DREAM?
Despite the wide use and success rate of ART (assisted reproductive technology) such as invitro fertilisation, artificial insemination with donor seed, gamete donation, embryo transfer andsurrogate motherhood, these technologies are not an option for many couples (fortechnical/biological/financial reasons and ethical/moral objections). As Grinion (2007:134)states: âThe irony is that, on the one hand, reproductive technologies offer hope wherepreviously none existed, while on the other hand they introduce a series of complex, expensive,and often morally troubling treatment modalities.â After having contemplated all alternativesfrom either a moral, ethical, economic or all-encompassing point of view, adoption is often theonly remaining alternative to couples who want a child and live the dream of being a family.South Africa has a long practice and well-researched history of adoption (De Bruyn, 1976; DeBruyn, 1989; De Vos, 1995; Lombard, 1976; Mouton, 1976; Pakati, 1984; Van Delft, 1983)
The Anatomy and Facets of Dynamic Policies
Information flow policies are often dynamic; the security concerns of a
program will typically change during execution to reflect security-relevant
events. A key challenge is how to best specify, and give proper meaning to,
such dynamic policies. A large number of approaches exist that tackle that
challenge, each yielding some important, but unconnected, insight. In this work
we synthesise existing knowledge on dynamic policies, with an aim to establish
a common terminology, best practices, and frameworks for reasoning about them.
We introduce the concept of facets to illuminate subtleties in the semantics of
policies, and closely examine the anatomy of policies and the expressiveness of
policy specification mechanisms. We further explore the relation between
dynamic policies and the concept of declassification.Comment: Technical Report of publication under the same name in Computer
Security Foundations (CSF) 201
Quantitative analysis of multi-periodic supply chain contracts with options via stochastic programming
We propose a stochastic programming approach for quantitative analysis of supply contracts, involving flexibility, between a buyer and a supplier, in a supply chain framework. Specifically, we consider the case of multi-periodic contracts in the face of correlated demands. To design such contracts, one has to estimate the savings or costs induced for both parties, as well as the optimal orders and commitments. We show how to model the stochastic process of the demand and the decision problem for both parties using the algebraic modeling language AMPL. The resulting linear programs are solved with a commercial linear programming solver; we compute the economic performance of these contracts, giving evidence that this methodology allows to gain insight into realistic problems.stochastic programming; supply contract; linear programming; modeling software; decision tree
- âŚ