Conditionally Optimal Weights of Evidence

A weight of evidence is a calibrated statistic whose values in [0,1] indicate the degree of agreement between the data and either of two hypothesis, one being treated as the null (H_0) and the other as the alternative (H_1). A value of zero means perfect agreement with the null, whereas a value of one means perfect agreement with the alternative. The optimality we consider is minimal mean squared error (MSE) under the alternative while keeping the MSE under the null below a fixed bound. This paper studies such statistics from a conditional point of view, in particular for location and scale models.     

Riferimenti isotropi in relatività generale

We consider anew approach for a relativistic frame of reference in the polar sense [1] (two-congruences) and the related non-holonomic techniques for anull congruence (light flux); 1° order characteristic tensors, Ricci rotation coefficients, longitudinal and transversal covariant derivatives are deduced in general form. Thus, the method of a standard frame of reference is extended to thenull case.

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Sunto Si consideraun nuovo approccio per un sistema di riferimento relativistico nel senso polare [1] (bicongruenza), adattando le tecniche non-olonome connesse al caso in cuiuna delle due congruenze sia nulla (flusso di luce); si derivano, in forma generale, i tensori caratteristici del 1° ordine, i coefficienti di rotazione di Ricci, le derivate covarianti longitudinali e trasversali. I metodi dei sistemi di riferimento standard vengono così estesi alcaso nullo, determinando unaalternativa tensoriale al cosidetto metodo (non reale) delle tetradi nulle [15].

     

Null Extensions and Generalized Inflations of Brandt Semigroups

Clarke and Monzo defined in [3] a construction called a generalized inflation of a semigroup. It is always the case that any inflation of a semigroup is a generalized inflation, and any generalized inflation of a semigroup is a null extension of the semigroup. Clarke and Monzo proved that any associative null extension of a base semigroup which is a union of groups is in fact a generalized inflation. In this paper we study null extensions and generalized inflations of Brandt semigroups. We first prove that any generalized inflation of a Brandt semigroup is actually an inflation of the semigroup. This answers a question posed by Clarke and Monzo in [3]. Then we characterize associative null extensions of Brandt semigroups, and show that there are associative null extensions of Brandt semigroups which are not generalized inflations.     

A new test on the conditional capital asset pricing model

Testing the validity of the conditional capital asset pricing model(CAPM) is a puzzle in the finance literatureLewellen and Nagel[14]find that the variation in betas and in the equity premium would have to be implausibly large to explain important asset-pricing anomaliesUnfortunately, they do not provide a rigorous test statisticBased on a simulation study, the method proposed in Lewellen and Nagel[14]tends to reject the null too frequently.We develop a new test procedure and derive its limiting distribution under the null hypothesis.Also, we provide a Bootstrap approach to the testing procedure to gain a good finite sample performanceBoth simulations and empirical studies show that our test is necessary for making correct inferences with the conditional CAPM.     

The discrete null space method for constrained mechanical systems in nonlinear structural and multibody dynamics

Corresponding to d'Alemberts principle in classical mechanics, the discrete null space method developed in [1] provides an energy-momentum conserving time stepping scheme for conservative finite-dimensional dynamical systems subject to constraints. The elimination of the Lagrange multipliers from the temporal discrete system leads to a reduced number of unknowns and to an improved condition number during the iterative solution of the nonlinear system. External and internal constraints are fulfilled likewise at the time nodes, wherefore the discrete null space method is particularly suited for the treatment of elastic multibody systems in structural dynamics. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A test for elliptical symmetry

This paper presents a statistic for testing the hypothesis of elliptical symmetry. The statistic also provides a specialized test of multivariate normality. We obtain the asymptotic distribution of this statistic under the null hypothesis of multivariate normality, and give a bootstrapping procedure for approximating the null distribution of the statistic under an arbitrary elliptically symmetric distribution. We present simulation results to examine the accuracy of the asymptotic distribution and the performance of the bootstrapping procedure. Finally, for selected alternatives, we compare the power of our test statistic with that of recently proposed tests for elliptical symmetry given by Manzotti et al. [A statistic for testing the null hypothesis of elliptical symmetry, J. Multivariate Anal. 81 (2002) 274-285] and Schott [Testing for elliptical symmetry in covariance-matrix-based analyses, Statist. Probab. Lett. 60 (2002) 395-404], and with that of the well known tests for multivariate normality of Mardia [Measures of multivariate skewness and kurtosis with applications, Biometrika 57 (1970) 519-530] and Baringhaus and Henze [A consistent test for multivariate normality based on the empirical characteristic function, Metrika 35 (1988) 339-348].     

The Algebraic Perturbation Method for Generalized Inverses

Algebraic perturbation methods were first proposed for the solution of nonsingular linear systems by R. E. Lynch and T. J. Aird [2]. Since then, the algebraic perturbation methods for generalized inverses have been discussed by many scholars [3]-[6]. In [4], a singular square matrix was perturbed algebraically to obtain a nonsingular matrix, resulting in the algebraic perturbation method for the Moore-Penrose generalized inverse. In [5], some results on the relations between nonsingular perturbations and generalized inverses of $m\times n$ matrices were obtained, which generalized the results in [4]. For the Drazin generalized inverse, the author has derived an algebraic perturbation method in [6]. In this paper, we will discuss the algebraic perturbation method for generalized inverses with prescribed range and null space, which generalizes the results in [5] and [6]. We remark that the algebraic perturbation methods for generalized inverses are quite useful. The applications can be found in [5] and [8]. In this paper, we use the same terms and notations as in [1].     

‘Duality’ of the Nikodym property and the Hahn property: Densities defined by sequences of matrices

The authors investigated in Boos and Leiger (2008) [5] the ‘duality’ of the Nikodym property (NP) of the set of all null sets of the density defined by any nonnegative matrix and the Hahn property (HP) of the strong null domain of it. In this paper, the investigation of the intimated duality is continued by considering densities defined by sequences of nonnegative matrices. These considerations are motivated by the known result that the ideal of the null sets of the uniform density has NP. In this context the general notion of S-convergence of double sequences (cf. Drewnowski, 2002 [8]) containing Pringsheim convergence, Hardy convergence and uniform convergence of double sequences is used.     

Chaos, self-organized criticality, and SETAR nonlinearity: An analysis of purchasing power parity between Canada and the United States

This paper uses monthly observations for the real exchange rate between Canada and the United States over the recent flexible exchange rate period (from January 1, 1973 to August 1, 2004) to test purchasing power parity between Canada and the United States using unit root and stationarity tests. Moreover, given the apparent random walk behavior in the real exchange rate, various tests from dynamical systems theory, such as for example, the Nychka et al. [Nychka DW, Ellner S, Ronald GA, McCaffrey D. Finding chaos in noisy systems. J Roy Stat Soc B 1992;54:399–426] chaos test, the Li [Li W. Absence of 1/f spectra in Dow Jones average. Int J Bifurcat Chaos 1991;1:583–97] self-organized criticality test, and the Hansen [Hansen, B.E. Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 1996;64:413–30] threshold effects test are used to distinguish between stochastic and deterministic origin for the real exchange rate.     

An alternative characterization of the weighted Banzhaf value

We provide a new characterization of the weighted Banzhaf value derived from some postulates in a recent paper by Radzik, Nowak and Driessen [7]. Our approach owes much to the work by Lehrer [4] on the classical Banzhaf value based on the idea of amalgamation of pairs of players and an induction construction of the value. Compared with the approach in [7] we consider two new postulates: a weighted version of Lehrer’s “2-efficiency axiom” [4] and a generalized “null player out” property studied in terms of symmetric games by Derks and Haller [2]. Received: December 1997/final version: October 1999     

Quasi-separatrix layers and three-dimensional reconnection diagnostics for line-tied tearing modes

In three-dimensional magnetic configurations for a plasma in which no closed field line or magnetic null exists, no magnetic reconnection can occur, by the strictest definition of reconnection. A finitely long pinch with line-tied boundary conditions, in which all the magnetic field lines start at one end of the system and proceed to the opposite end, is an example of such a system. Nevertheless, for a long system of this type, the physical behavior in resistive magnetohydrodynamics (MHD) essentially involves reconnection. This has been explained in terms comparing the geometric and tearing widths [1] and [2]. The concept of a quasi-separatrix layer [3] and [4] was developed for such systems. In this paper we study a model for a line-tied system in which the corresponding periodic system has an unstable tearing mode. We analyze this system in terms of two magnetic field line diagnostics, the squashing factor [5], [6] and [7] and the electrostatic potential difference [8] and [9] which has been used in kinematic reconnection studies. We discuss the physical and geometric significance of these two diagnostics and compare them in the context of discerning tearing-like (reconnection-like) behavior in line-tied modes.     

On a semi-Markov generalization of the random walk

The semi-Markov process studied here is a generalized random walk on the non-negative integers with zero as a reflecting barrier, in which the time interval between two consecutive jumps is given an arbitrary distribution H(t). Our process is identical with the Markov chain studied by Miller [6] in the special case when H(t)=U₁(t), the Heaviside function with unit jump at t=1. By means of a Spitzer-Baxter type identity, we establish criteria for transience, positive and null recurrence, as well as conditions for exponential ergodicity. The results obtained here generalize those of [6] and some classical results in random walk theory [10].     

Nonparametric tests for multiple regression under progressive censoring

For continuous observations from time-sequential studies, suitable Cramér-von Mises and Kolmogorov-Smirnov types of (nonparametric) statistics (based on linear rank statistics) for testing hypotheses on some multiple-regression models are proposed and studied. The asymptotic theory of these tests is provided for both the null and (local) alternative hypotheses situations and is based on the weak convergence of suitable rank order processes (on the D[0, 1] space) to certain functions of Brownian motions. Bahadur efficiency results are also presented. Empirical values of the percentile points of the null distributions of the proposed test statistics, obtained through simulation studies, are also provided.     

Wedge removability of metrically thin sets and application to the CR-meromorphic extension

We give a wedge removability theorem for metrically thin sets of two codimensional Hausdorff null measure. Following [22], this removability theorem combined with the wedge removability theorem of [21] for closed subsets of two codimensional manifolds, gives a CR-meromorphic extension theorem in the greater codimensional case. Received: 28 August 1999; in final form: 10 April 2000 / Published online: 17 May 2001     

Submanifolds in de sitter space-time satisfying ΔH=λH

In [3] the author initiated the study of submanifolds whose mean curvature vectorH is an eigenvector of the Laplacian Δ and proved that such submanifolds are either biharmonic or of 1-type or of null 2-type. The classification of surfaces with ΔH=λH in a Euclidean 3-space was done by the author in 1988. Moreover, in [4] the author classified such submanifolds in hyperbolic spaces. In this article we study this problem for space-like submanifolds of the Minkowski space-timeE ₁ ^m when the submanifolds lie in a de Sitter space-time. As a result, we characterize and classify such submanifolds in de Sitter space-times.     

Badly approximablep-adic integers

It is known that thep-adic integers that are badly approximable by rationals form a null set with respect to Haar measure. We define a [0,1]-valued dimension function on thep-adic integers analogous to Hausdorff dimension inR and show that with respect to this function the dimension of the set of badly approximablep-adic integers is 1.     

Components of the Pearson-Fisher Chi-squared Statistic

The Pearson-Fisher chi-squared test can be used to evaluate the goodness-of-fit of categorized continuous data with known bin endpoints compared to a continuous distribution, in the presence of unknown (nuisance) distribution parameters. Rayner and McAlevey [11] and Rayner and Best [9], [10] demonstrate that in this case, component tests of the Pearson-Fisher chi-squared test statistic can be obtained by equating it to the Neyman smooth score test for a categorized composite null hypothesis under certain restrictions. However, only Rayner and McAlevey [11] provide even brief details as to how these restrictions can be used to obtain any kind of decomposition. More importantly, the relationship between the range of possible decompositions and the interpretation of the corresponding test statistic components has not previously been investigated. This paper provides the necessary details, as well as an overview of the decomposition options available, and revisits two published examples.     

Theory and computation of restricted linear models

Least squares inverses and complementary matrices are used to develop a comprehensive theory of estimation for a restricted linear model. Testable hypotheses as defined in Searle [8] are extended to involve nonestimable functions. An explicit expression for the sum of squares of deviation from the null hypothesis under the general setup with restrictions (Rao [7, p. 242]) and the corresponding number of degrees of freedom are obtained for implementation on computers.     

Null controllability of von Kármán thermoelastic plates under the clamped or free mechanical boundary conditions

In this paper, we provide results of local and global null controllability for 2-D thermoelastic systems, in the absence of rotational inertia, and under the influence of the (nonLipschitz) von Kármán nonlinearity. The plate component may be taken to satisfy either the clamped or higher order (and physically relevant) free boundary conditions. In the accompanying analysis, critical use is made of sharp observability estimates which obtain for the linearization of the thermoelastic plate (these being derived in [G. Avalos, I. Lasiecka, The null controllability of thermoelastic plates and singularity of the associated minimal energy function, J. Math. Anal. Appl. 294 (2004) 34-61] and [G. Avalos, I. Lasiecka, Asymptotic rates of blowup for the minimal energy function for the null controllability of thermoelastic plates: The free case, in: Proc. of the Conference for the Control of Partial Differential Equations, Georgetown University, Dekker, in press]). Moreover, another key ingredient in our work to steer the given nonlinear dynamics is the recent result in [A. Favini, M.A. Horn, I. Lasiecka, D. Tataru, Addendum to the paper: Global existence, uniqueness and regularity of solution to a von Kármán system with nonlinear boundary dissipation, Differential Integral Equations 10 (1997) 197-200] concerning the sharp regularity of the von Kármán nonlinearity.     

The characterization of compact operators on spaces of strongly summable and bounded sequences

We use the characterizations of the classes of all infinite matrices that map the spaces of sequences which are strongly summable or bounded by the Cesàro method of order 1 into the spaces of null or convergent sequences given by Ba?ar, Malkowsky and Altay [Matrix transformations on the matrix domains of triangles in the spaces of strongly C₁-summable and bounded sequences, Publ. Math. Debrecen 73 (1-2) (2008), 193-213] and the Hausdorff measure of noncompactness to characterize the classes of all compact operators between those spaces.