Skovgaard`s adjustment to likelihood ratio tests in exponential family nonlinear models

Likelihood ratio tests can be substantially size distorted in small- and moderate-sized samples. In this paper, we apply Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-321] adjusted likelihood ratio statistic to exponential family nonlinear models. We show that the adjustment term has a simple compact form that can be easily implemented from standard statistical software. The adjusted statistic is approximately distributed as X(2) with high degree of accuracy. It is applicable in wide generality since it allows both the parameter of interest and the nuisance parameter to be vector-valued. Unlike the modified profile likelihood ratio statistic obtained from Cox and Reid [Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference. journal of the Royal Statistical Society B49, 1-39], the adjusted statistic proposed here does not require an orthogonal parameterization. Numerical comparison of likelihood-based tests of varying dispersion favors the test we propose and a Bartlett-corrected version of the modified profile likelihood ratio test recently obtained by Cysneiros and Ferrari [Cysneiros, A.H.M.A., Ferrari, S.L.P., 2006. An improved likelihood ratio test for varying dispersion in exponential family nonlinear models. Statistics and Probability Letters 76 (3), 255-265]. (C) 2008 Elsevier B.V. All rights reserved.

Stability of periodic optical solitons for a nonlinear Schrodinger system

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrodinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minima period. We also establish global well posedness for our system by using Bourgain`s approach.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

Influence diagnostics in Birnbaum-Saunders nonlinear regression models

We consider the issue of assessing influence of observations in the class of Birnbaum-Saunders nonlinear regression models, which is useful in lifetime data analysis. Our results generalize those in Galea et al. [8] which are confined to Birnbaum-Saunders linear regression models. Some influence methods, such as the local influence, total local influence of an individual and generalized leverage are discussed. Additionally, the normal curvatures for studying local influence are derived under some perturbation schemes. We also give an application to a real fatigue data set.

A note on influence diagnostics in nonlinear mixed-effects elliptical models

This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the A matrices (required for the assessment of local influence) for a quite general model which includes the one proposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leverage on fixed and random effects. The matrix formulation has notational advantages, since despite the complexity of the postulated model, all general formulas are compact, clear and have nice forms. (C) 2010 Elsevier B.V. All rights reserved.

Asymptotic skewness in Birnbaum-Saunders nonlinear regression models

The family of distributions proposed by Birnbaum and Saunders (1969) can be used to model lifetime data and it is widely applicable to model failure times of fatiguing materials. We give a simple matrix formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in Birnbaum-Saunders nonlinear regression models, recently introduced by Lemonte and Cordeiro (2009). The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors, in order to obtain closed-form skewness in a wide range of nonlinear regression models. Empirical and real applications are analyzed and discussed. (C) 2010 Elsevier B.V. All rights reserved.

Birnbaum-Saunders nonlinear regression models

We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [Rieck, J.R., Nedelman, J.R., 1991. A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33, 51-60]. We discuss maximum-likelihood estimation for the parameters of the model, and derive closed-form expressions for the second-order biases of these estimates. Our formulae are easily computed as ordinary linear regressions and are then used to define bias corrected maximum-likelihood estimates. Some simulation results show that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. Two empirical applications are analysed and discussed. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n(-1/2) for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. (C) 2010 Elsevier B.V. All rights reserved.

Tempol ameliorates murine viral encephalomyelitis by preserving the blood-brain barrier, reducing viral load, and lessening inflammation

Multiple sclerosis (MS) is a progressive inflammatory and/or demyelinating disease of the human central nervous system (CNS). Most of the knowledge about the pathogenesis of MS has been derived from murine models, such as experimental autoimmune encephalomyelitis and vital encephalomyelitis. Here, we infected female C57BL/6 mice with a neurotropic strain of the mouse hepatitis virus (MHV-59A) to evaluate whether treatment with the multifunctional antioxidant tempol (4-hydroxy-2,2,6,6-tetramethyl-1-piperidinyloxy) affects the ensuing encephalomyelitis. In untreated animals, neurological symptoms developed quickly: 90% of infected mice died 10 days after virus inoculation and the few survivors presented neurological deficits. Treatment with tempol (24 mg/kg, ip, two doses on the first day and daily doses for 7 days plus 2 mM tempol in the drinking water ad libitum) profoundly altered the disease outcome: neurological symptoms were attenuated, mouse survival increased up to 70%, and half of the survivors behaved as normal mice. Not Surprisingly, tempol substantially preserved the integrity of the CNS, including the blood-brain barrier. Furthermore, treatment with tempol decreased CNS vital titers, macrophage and T lymphocyte infiltration, and levels of markers of inflammation, such as expression of inducible nitric oxide synthase, transcription of tumor necrosis factor-alpha and interferon-gamma, and protein nitration. The results indicate that tempol ameliorates murine viral encephalomyelitis by altering the redox status of the infectious environment that contributes to an attenuated CNS inflammatory response. overall, our study supports the development of therapeutic strategies based on nitroxides to manage neuroinflammatory diseases, including MS. (C) 2009 Elsevier Inc. All rights reserved.

Nickel catalysts supported on ZrO2, Y2O3-stabilized ZrO2 and CaO-stabilized ZrO2 for the steam reforming of ethanol: Effect of the support and nickel load

Catalysts with various nickel loads were prepared on supports of ZrO2, ZrO2-Y2O3 and ZrO2-CaO, characterized by XRD and TPR and tested for activity in ethanol steam reforming. XRD of the supports identified the monoclinic crystalline phase in the ZrO2 and cubic phases in the ZrO2-Y2O3 and ZrO2-CaO supports. In the catalysts, the nickel impregnated on the supports was identified as the NiO phase. In the TPR analysis, peaks were observed showing the NiO phase having different interactions with the supports. In the catalytic tests, practically all the catalysts achieved 100% ethanol conversion, H-2 yield was near 70% and the gaseous concentrations of the other co-products varied in accordance with the equilibrium among them, affected principally by the supports. It was observed that when the ZrO2 was modified with Y2O3 and CaO, there were big changes in the CO and CO2 concentrations, which were attributed to the rise in the number of oxygen vacancies, permitting high-oxygen mobility and affecting the gaseous equilibrium. The liquid products analysis showed a low selectivity to liquid co-products during the reforming reactions. (c) 2007 Published by Elsevier B.V.