An adaptive estimator of the memory parameter and the goodness-of-fit test using a multidimensional increment ratio statistic

The increment ratio (IR) statistic was first defined and studied in Surgailis et al. (2007) [19] for estimating the memory parameter either of a stationary or an increment stationary Gaussian process. Here three extensions are proposed in the case of stationary processes. First, a multidimensional central limit theorem is established for a vector composed by several IR statistics. Second, a goodness-of-fit χ²-type test can be deduced from this theorem. Finally, this theorem allows to construct adaptive versions of the estimator and the test which are studied in a general semiparametric frame. The adaptive estimator of the long-memory parameter is proved to follow an oracle property. Simulations attest to the interesting accuracies and robustness of the estimator and the test, even in the non Gaussian case.     

On the sector condition and homogenization of diffusions with a Gaussian drift

In this paper we present the functional central limit theorem for a class of Markov processes, whose L²-generator satisfies the so-called graded sector condition. We apply the result to obtain homogenization theorems for certain classes of diffusions with a random Gaussian drift. Additionally, we present a result concerning the regularity of the effective diffusivity tensor with respect to the parameters related to the statistics of the drift. The abstract central limit theorem, see Theorem 2.2, is obtained by applying the technique used in Sethuraman et al. (Comm. Pure Appl. Math. 53 (2000) 972) to the case of infinite particle systems.     

Une preuve alternative de l'existence d'un équilibre de Nash dans les jeux discontinus

This Note presents a theorem of the existence of the Nash equilibrium for discontinuous games in a topological vector space. We will use an assumption of better reply secure which is stronger then that of Reny. If the payoff function is upper semi-continuous, the two assumptions coincide. Our proof is simple, independent and based on a version of Fan–Browder theorem of existence of maximal element due to Deguire and Lassonde, which is extended to the non-Hausdorf case. To cite this article: J.-M. Bonnisseau et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Some Applications of the Hodge-de Rham Decomposition to Ricci Solitons

The aim of this paper is to present a link between the Perelman potential for a compact Ricci soliton M ⁿ and the Hodge-de Rham decomposition theorem, we shall use this result to present an integral formula which enables us to establish conditions under which the Ricci soliton is trivial. Moreover, given a Ricci soliton such that its associated vector field X is a conformal vector field we show that in the compact case X is a Killing vector field, while for the non-compact case, either the soliton is Gaussian or X is a Killing vector field.     

关于向量优化问题的Δ函数标量化刻画的某些注记

近期,夏远梅等(重庆师范大学（自然科学版）,2015,32(1):12-15)利用Δ函数通过非线性标量化方法研究了向量优化问题的?-真有效解并举例说明了主要结果.笔者指出:其定理1是Gao等(Journal of Industrial and Management Optimization,2011,7（2）: 483-496)建立的定理4.6(i)的特例;其定理2的证明存在不足.通过研究一般的(C,ε)-真有效解的Δ函数非线性标量化,给出了定理2的严谨证明.最后,在?-真有效解存在的情况下举例说明了主要结果.     

Pták Homomorphism Theorem Revisited

Rodrigues' extension (1989) of the classical Pták's homomoiphism theorem to a non-necessarily locally convex setting stated that a nearly semi-open mapping between a semi-B-complete space and an arbitrary topoiogical vector space is semi-open. In this paper we study this extension and, as a consequence of the results obtained, provide an improvement of Pták's homomorphism theorem.     

A general Isserlis theorem for mixed-Gaussian random variables

This work generalizes a widely used result derived by L. Isserlis for the expectations of products of jointly Gaussian random variables by extending it to include mixed-Gaussian random variables.     

Core equivalences for equilibria supported by non-linear prices

The goal of this paper is to provide some new cooperative characterizations and optimality properties of competitive equilibria supported by non-linear prices. The general framework is that of economies whose commodity space is an ordered topological vector space which need not be a vector lattice. The central notion of equilibrium is the one of personalized equilibrium introduced by Aliprantis et al. (J Econ Theory 100:22–72, 2001). Following Herves-Beloso and Moreno-Garcia (J Math Econ 44:697–706, 2008), the veto power of the grand coalition is exploited in the original economy and in a suitable family of economies associated to the original one. The use of Aubin coalitions allows us to connect results with the arbitrage free condition due to non-linear supporting prices. The use of rational allocations allows us to dispense with Lyapunov convexity theorem. Applications are provided in connection with strategic market games and economies with asymmetric information.     

Corrigendum to “The envelope theorem for multiobjective convex programming via contingent derivatives” [J. Math. Anal. Appl. 372 (1) (2010) 197–207]

The aim of this note is to formulate an envelope theorem for vector convex programs. This version corrects an earlier work, “The envelope theorem for multiobjective convex programming via contingent derivatives” by Jiménez Guerra et al. (2010) [3]. We first propose a necessary and sufficient condition allowing to restate the main result proved in the alluded paper. Second, we introduce a new Lagrange multiplier in order to obtain an envelope theorem avoiding the aforementioned error.     

Graphical tools for model-based mixture discriminant analysis

The paper introduces a methodology for visualizing on a dimension reduced subspace the classification structure and the geometric characteristics induced by an estimated Gaussian mixture model for discriminant analysis. In particular, we consider the case of mixture of mixture models with varying parametrization which allow for parsimonious models. The approach is an extension of an existing work on reducing dimensionality for model-based clustering based on Gaussian mixtures. Information on the dimension reduction subspace is provided by the variation on class locations and, depending on the estimated mixture model, on the variation on class dispersions. Projections along the estimated directions provide summary plots which help to visualize the structure of the classes and their characteristics. A suitable modification of the method allows us to recover the most discriminant directions, i.e., those that show maximal separation among classes. The approach is illustrated using simulated and real data.     

Principal points of a multivariate mixture distribution

A set of n-principal points of a distribution is defined as a set of n points that optimally represent the distribution in terms of mean squared distance. It provides an optimal n-point-approximation of the distribution. However, it is in general difficult to find a set of principal points of a multivariate distribution. Tarpey et al. [T. Tarpey, L. Li, B. Flury, Principal points and self-consistent points of elliptical distributions, Ann. Statist. 23 (1995) 103-112] established a theorem which states that any set of n-principal points of an elliptically symmetric distribution is in the linear subspace spanned by some principal eigenvectors of the covariance matrix. This theorem, called a “principal subspace theorem”, is a strong tool for the calculation of principal points. In practice, we often come across distributions consisting of several subgroups. Hence it is of interest to know whether the principal subspace theorem remains valid even under such complex distributions. In this paper, we define a multivariate location mixture model. A theorem is established that clarifies a linear subspace in which n-principal points exist.     

Grauert- and Lax-Halmos-type theorems and extension of matrices with entries in H

In the paper we prove an extension theorem for matrices with entries in H^∞(U) for U a Riemann surface of a special type. One of the main components of the proof is a Grauert-type theorem for “holomorphic” vector bundles defined on maximal ideal spaces of certain Banach algebras.     

Approximation of the occupation measure of Lévy processes

Consider a real-valued Lévy process with non-zero Gaussian component and jumps with locally finite variation. We obtain an invariance principle theorem for the speed of approximation of its occupation measure by means of functionals defined on regularizations of the paths. This theorem is a first extension to processes with jumps of previous results for semimartingales with continuous paths. To cite this article: E. Mordecki, M. Wschebor, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Orthogonality Matrices for Modules over Finite Frobenius Rings and MacWilliams' Equivalence Theorem

MacWilliams' equivalence theorem states that Hamming isometries between linear codes extend to monomial transformations of the ambient space. One of the most elegant proofs for this result is due to K. P. Bogart et al. (1978, Inform. and Control37, 19–22) where the invertibility of orthogonality matrices of finite vector spaces is the key step. The present paper revisits this technique in order to make it work in the context of linear codes over finite Frobenius rings.     

Tail asymptotics for the queue size distribution in the MAP/G/1 retrial queue

We consider a MAP/G/1 retrial queue where the service time distribution has a finite exponential moment. We derive matrix differential equations for the vector probability generating functions of the stationary queue size distributions. Using these equations, Perron–Frobenius theory, and the Karamata Tauberian theorem, we obtain the tail asymptotics of the queue size distribution. The main result on light-tailed asymptotics is an extension of the result in Kim et al. (J. Appl. Probab. 44:1111–1118, 2007) on the M/G/1 retrial queue.     

Improved bounds for the Laplacian energy of Bethe trees

For k, d?2, a Bethe tree is a rooted tree with k levels which the root vertex has degree d, the vertices from level 2 to k-1 have degree d+1 and the vertices at the level k are pendent vertices. So et al, using a theorem by Ky Fan have obtained both upper and lower bounds for the Laplacian energy of bipartite graphs. We shall employ the above mentioned theorem to obtain new and improved bounds for the Laplacian energy in the case of Bethe trees.     

Nonstandard integration theory in topological vector lattices

This paper develops a Daniell-Stone integration theory in topological vector lattices. Starting with an internal, vector valued, positive linear functionalI on an internal lattice of vector valued functions, we produce a nonstandard hull valued integralJ satisfying the monotone convergence theorem. Nonstandard hulls form a natural extension of infinite dimensional spaces and are equivalent to Banach space ultrapower constructions. The first application of our integral is a construction of Banach limits for bounded, vector valued sequences. The second example yields an integral representation for bounded and quasibounded harmonic functions similar to that of the Martin boundary. The third application uses our general integral to extend the Bochner integral.     

Bankruptcy problems with two references: an impartial compromise

Pulido et al. (Annals Oper Res 158:133–141, 2008) present an extension of the classical bankruptcy problem (O’Neill in Math Social Sci 2:345–371, 1982) where the involved agents have, apart from the claims vector, an additional reference vector. To analyze this extended problem, they propose the extreme and the diagonal approaches, both of them restricted to the case in which the reference vector is lower than the claims vector. We note that if the claims and the reference vectors are interchanged, the allocation proposed by the extreme approach varies. Therefore, by introducing the idea of impartiality, in the current approach, we propose an extension of their model in which no relation is assumed between the claims and reference vectors.     

A note on rates of convergence in the multidimensional CLT for maximum partial sums

In this note we obtain rates of convergence in the central limit theorem for certain maximum of coordinate partial sums of independent identically distributed random vectors having positive mean vector and a nonsingular correlation matrix. The results obtained are in terms of rates of convergence in the multidimensional central limit theorem. Thus under the conditions of Sazonov (1968, Sankhya, Series A30 181–204, Theorem 2), we have the same rate of convergence for the vector of coordinate maximums. Other conditions for the multidimensional CLT are also discussed, c.f., Bhattachaya (1977, Ann. Probability 5 1–27). As an application of one of the results we obtain a multivariate extension of a theorem of Rogozin (1966, Theor. Probability Appl. 11 438–441).     

On the structure of p-adic subanalytic functions and sets

We prove a p-adic version of the Lion?CRolin preparation theorem. As a consequence, we obtain a cell decomposition theorem, which can be viewed as an extension of Denef??s cell decomposition theorem to the p-adic analytic case. Using these theorems, we give shorter and more explicit proofs of some of the results by Denef and van den Dries on p-adic subanalytic sets.