Search results for " statistics"
showing 10 items of 1891 documents
Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction
2020
We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Caratheodory terms. One is parametric, $$(p-1)$$-sublinear with a partially concave nonlinearity near zero. The other is $$(p-1)$$-superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter $$\lambda >0$$ varies.
Modeling Spatial Data Pooled over Time: Schematic Representation and Monte Carlo Evidences
2015
The spatial autocorrelation issue is now well established, and it is almost impossible to deal with spatial data without considering this reality. In addition, recent developments have been devoted to developing methods that deal with spatial autocorrelation in panel data. However, little effort has been devoted to dealing with spatial data (cross-section) pooled over time. This paper endeavours to bridge the gap between the theoretical modeling development and the application based on spatial data pooled over time. The paper presents a schematic representation of how spatial links can be expressed, depending on the nature of the variable, when combining the spatial multidirectional relatio…
Extension of The Stochastic Differential Calculus To Complex Processes
1996
In structural engineering complex processes arise to predict the first excursion failure, fatigue failure, etc. Indeed to solve these problems the envelope function, which is the modulus of a complex process, is usually introduced. In this paper the statistics of the complex response process related to the envelope statistics of linear systems subjected to parametric stationary normal white noise input are evaluated by using extensively the properties of stochastic differential calculus.
Topology-based goodness-of-fit tests for sliced spatial data
2023
In materials science and many other application domains, 3D information can often only be extrapolated by taking 2D slices. In topological data analysis, persistence vineyards have emerged as a powerful tool to take into account topological features stretching over several slices. In the present paper, we illustrate how persistence vineyards can be used to design rigorous statistical hypothesis tests for 3D microstructure models based on data from 2D slices. More precisely, by establishing the asymptotic normality of suitable longitudinal and cross-sectional summary statistics, we devise goodness-of-fit tests that become asymptotically exact in large sampling windows. We illustrate the test…
Optimal rates of convergence for persistence diagrams in Topological Data Analysis
2013
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results.
Population Monte Carlo Schemes with Reduced Path Degeneracy
2017
Population Monte Carlo (PMC) algorithms are versatile adaptive tools for approximating moments of complicated distributions. A common problem of PMC algorithms is the so-called path degeneracy; the diversity in the adaptation is endangered due to the resampling step. In this paper we focus on novel population Monte Carlo schemes that present enhanced diversity, compared to the standard approach, while keeping the same implementation structure (sample generation, weighting and resampling). The new schemes combine different weighting and resampling strategies to reduce the path degeneracy and achieve a higher performance at the cost of additional low computational complexity cost. Computer si…
A saturated strategy robustly ensures stability of the cooperative equilibrium for Prisoner's dilemma
2016
We study diffusion of cooperation in a two-population game in continuous time. At each instant, the game involves two random individuals, one from each population. The game has the structure of a Prisoner's dilemma where each player can choose either to cooperate (c) or to defect (d), and is reframed within the field of approachability in two-player repeated game with vector payoffs. We turn the game into a dynamical system, which is positive, and propose a saturated strategy that ensures local asymptotic stability of the equilibrium (c, c) for any possible choice of the payoff matrix. We show that there exists a rectangle, in the space of payoffs, which is positively invariant for the syst…
The shape of small sample biases in pricing kernel estimations
2016
AbstractNumerous empirical studies find pricing kernels that are not-monotonically decreasing; the findings are at odds with the pricing kernel being marginal utility of a risk-averse, so-called representative agent. We study in detail the common procedure which estimates the pricing kernel as the ratio of two separate density estimations. In the first step, we analyse theoretically the functional dependence for the ratio of a density to its estimated density; this cautions the reader regarding potential computational issues coupled with statistical techniques. In the second step, we study this quantitatively; we show that small sample biases shape the estimated pricing kernel, and that est…
Learning spatial filters for multispectral image segmentation.
2010
International audience; We present a novel filtering method for multispectral satel- lite image classification. The proposed method learns a set of spatial filters that maximize class separability of binary support vector machine (SVM) through a gradient descent approach. Regularization issues are discussed in detail and a Frobenius-norm regularization is proposed to efficiently exclude uninformative filters coefficients. Experiments car- ried out on multiclass one-against-all classification and tar- get detection show the capabilities of the learned spatial fil- ters.
The effect of automated taxa identification errors on biological indices
2017
In benthic macroinvertebrate biomonitoring systems, the target is to determine the status of ecosystems based on several biological indices. To increase cost-efficiency, computer-based taxa identification for image data has recently been developed. Taxa identification errors can, however, have strong effects on the indices and thus on the determination of the ecological status. In order to shift the biomonitoring process towards automated expert systems, we need a clear understanding on the bias caused by automation. In this paper, we examine eleven classification methods in the case of macroinvertebrate image data and show how their classification errors propagate into different biological…