7,702 research outputs found
Computation of an exact confidence set for a maximum point of a univariate polynomial function in a given interval
Construction of a confidence set for a maximum point of a function is an important statistical problem. Wan et al., (2015) provided an exact 1−α1−α confidence set for a maximum point of a univariate polynomial function in a given interval. In this paper, we give an efficient computational method for computing the confidence set of Wan et al., (2015). We demonstrate with two examples that the new method is substantially more efficient than the proposals by Wan et al., (2015). Matlab programs have been written which make the implementation of the new method straightforward
Confidence sets for optimal factor levels of a response surface
Construction of confidence sets for the optimal factor levels is an important topic in response surfaces methodology. In Wan et al. (2015), an exact inline image confidence set has been provided for a maximum or minimum point (i.e., an optimal factor level) of a univariate polynomial function in a given interval. In this article, the method has been extended to construct an exact inline image confidence set for the optimal factor levels of response surfaces. The construction method is readily applied to many parametric and semiparametric regression models involving a quadratic function. A conservative confidence set has been provided as an intermediate step in the construction of the exact confidence set. Two examples are given to illustrate the application of the confidence sets. The comparison between confidence sets indicates that our exact confidence set is better than the only other confidence set available in the statistical literature that guarantees the inline image confidence level
Confidence sets for optimal factor levels of a response surface
Construction of confidence sets for the optimal factor levels is an important topic in response surfaces methodology. In Wan et al. (2015), an exact (1 - a) confidence set has been provided for a maximum or minimum point (i.e., an optimal factor level) of a univariate polynomial function in a given interval. In this article, the method has been extended to construct an exact (1 - a) confidence set for the optimal factor levels of response surfaces. The construction method is readily applied to many parametric and semiparametric regression models involving a quadratic function. A conservative confidence set has been provided as an intermediate step in the construction of the exact confidence set. Two examples are given to illustrate the application of the confidence sets. The comparison between confidence sets indicates that our exact confidence set is better than the only other confidence set available in the statistical literature that guarantees the (1 - a) confidence level
Determination of Bootstrap confidence intervals on sensitivity indices obtained by polynomial chaos expansion
L’analyse de sensibilité a pour but d’évaluer l’influence de la variabilité d’un ou plusieurs paramètres d’entrée d’un modèle sur la variabilité d’une ou plusieurs réponses. Parmi toutes les méthodes d’approximations, le développement sur une base de chaos polynômial est une des plus efficace pour le calcul des indices de sensibilité, car ils sont obtenus analytiquement grâce aux coefficients de la décomposition (Sudret (2008)). Les indices sont donc approximés et il est difficile d’évaluer l’erreur due à cette approximation. Afin d’évaluer la confiance que l’on peut leur accorder nous proposons de construire des intervalles de confiance par ré-échantillonnage Bootstrap (Efron, Tibshirani (1993)) sur le plan d’expérience utilisé pour construire l’approximation par chaos polynômial. L’utilisation de ces intervalles de confiance permet de trouver un plan d’expérience optimal garantissant le calcul des indices de sensibilité avec une précision donnée
Open TURNS: An industrial software for uncertainty quantification in simulation
The needs to assess robust performances for complex systems and to answer
tighter regulatory processes (security, safety, environmental control, and
health impacts, etc.) have led to the emergence of a new industrial simulation
challenge: to take uncertainties into account when dealing with complex
numerical simulation frameworks. Therefore, a generic methodology has emerged
from the joint effort of several industrial companies and academic
institutions. EDF R&D, Airbus Group and Phimeca Engineering started a
collaboration at the beginning of 2005, joined by IMACS in 2014, for the
development of an Open Source software platform dedicated to uncertainty
propagation by probabilistic methods, named OpenTURNS for Open source Treatment
of Uncertainty, Risk 'N Statistics. OpenTURNS addresses the specific industrial
challenges attached to uncertainties, which are transparency, genericity,
modularity and multi-accessibility. This paper focuses on OpenTURNS and
presents its main features: openTURNS is an open source software under the LGPL
license, that presents itself as a C++ library and a Python TUI, and which
works under Linux and Windows environment. All the methodological tools are
described in the different sections of this paper: uncertainty quantification,
uncertainty propagation, sensitivity analysis and metamodeling. A section also
explains the generic wrappers way to link openTURNS to any external code. The
paper illustrates as much as possible the methodological tools on an
educational example that simulates the height of a river and compares it to the
height of a dyke that protects industrial facilities. At last, it gives an
overview of the main developments planned for the next few years
Most Likely Transformations
We propose and study properties of maximum likelihood estimators in the class
of conditional transformation models. Based on a suitable explicit
parameterisation of the unconditional or conditional transformation function,
we establish a cascade of increasingly complex transformation models that can
be estimated, compared and analysed in the maximum likelihood framework. Models
for the unconditional or conditional distribution function of any univariate
response variable can be set-up and estimated in the same theoretical and
computational framework simply by choosing an appropriate transformation
function and parameterisation thereof. The ability to evaluate the distribution
function directly allows us to estimate models based on the exact likelihood,
especially in the presence of random censoring or truncation. For discrete and
continuous responses, we establish the asymptotic normality of the proposed
estimators. A reference software implementation of maximum likelihood-based
estimation for conditional transformation models allowing the same flexibility
as the theory developed here was employed to illustrate the wide range of
possible applications.Comment: Accepted for publication by the Scandinavian Journal of Statistics
2017-06-1
Why Are Beveridge-Nelson and Unobserved-Component Decompositions of GDP So Different?
This paper reconciles two widely-used decompositions of GDP into trend and cycle that yield starkly different results. Beveridge-Nelson (BN) implies that a stochastic trend accounts for most of the variation in output, while Unobserved-Components (UC) implies cyclical variation is dominant. Which is correct has broad implications for the relative importance of real versus nominal shocks. We show the difference arises from the restriction imposed in UC that trend and cycle innovations are uncorrelated. When this restriction is relaxed, the UC decomposition is identical to the BN decomposition. Furthermore, the zero correlation restriction can be rejected for U.S. quarterly GDP, with the estimated correlation being –0.9.
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