The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n(-1/2), n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.

A note on the local power of the LR, Wald, score and gradient tests

This paper examines the local power of the likelihood ratio, Wald, score and gradient tests under the presence of a scalar parameter, phi say, that is orthogonal to the remaining parameters. We show that some of the coefficients that define the local powers remain unchanged regardless of whether phi is known or needs to be estimated, where as the others can be written as the sum of two terms, the first of which being the corresponding term obtained as if phi were known, and the second, an additional term yielded by the fact that phi is unknown. The contribution of each set of parameters on the local powers of the tests can then be examined. Various implications of our main result are stated and discussed. Several examples are presented for illustrative purposes

Local power and size properties of the LR, Wald, score and gradient tests in dispersion models

We derive asymptotic expansions for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of dispersion models, under a sequence of Pitman alternatives. The asymptotic distributions of these statistics are obtained for testing a subset of regression parameters and for testing the precision parameter. Based on these nonnull asymptotic expansions, the power of all four tests, which are equivalent to first order, are compared. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2012 Elsevier B.V. All rights reserved.

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the non-null distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present two empirical applications. (C) 2010 Elsevier B.V. All rights reserved.

Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples

The two-parameter Birnbaum-Saunders distribution has been used successfully to model fatigue failure times. Although censoring is typical in reliability and survival studies, little work has been published on the analysis of censored data for this distribution. In this paper, we address the issue of performing testing inference on the two parameters of the Birnbaum-Saunders distribution under type-II right censored samples. The likelihood ratio statistic and a recently proposed statistic, the gradient statistic, provide a convenient framework for statistical inference in such a case, since they do not require to obtain, estimate or invert an information matrix, which is an advantage in problems involving censored data. An extensive Monte Carlo simulation study is carried out in order to investigate and compare the finite sample performance of the likelihood ratio and the gradient tests. Our numerical results show evidence that the gradient test should be preferred. Further, we also consider the generalized Birnbaum-Saunders distribution under type-II right censored samples and present some Monte Carlo simulations for testing the parameters in this class of models using the likelihood ratio and gradient tests. Three empirical applications are presented. (C) 2011 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.

Testes em modelos weibull na forma estendida de Marshall-Olkin

In survival analysis, the response is usually the time until the occurrence of an event of interest, called failure time. The main characteristic of survival data is the presence of censoring which is a partial observation of response. Associated with this information, some models occupy an important position by properly fit several practical situations, among which we can mention the Weibull model. Marshall-Olkin extended form distributions other a basic generalization that enables greater exibility in adjusting lifetime data. This paper presents a simulation study that compares the gradient test and the likelihood ratio test using the Marshall-Olkin extended form Weibull distribution. As a result, there is only a small advantage for the likelihood ratio test

Testes de hipóteses em modelos de sobrevivência com Fração de cura

Survival models deals with the modeling of time to event data. However in some situations part of the population may be no longer subject to the event. Models that take this fact into account are called cure rate models. There are few studies about hypothesis tests in cure rate models. Recently a new test statistic, the gradient statistic, has been proposed. It shares the same asymptotic properties with the classic large sample tests, the likelihood ratio, score and Wald tests. Some simulation studies have been carried out to explore the behavior of the gradient statistic in fi nite samples and compare it with the classic statistics in diff erent models. The main objective of this work is to study and compare the performance of gradient test and likelihood ratio test in cure rate models. We first describe the models and present the main asymptotic properties of the tests. We perform a simulation study based on the promotion time model with Weibull distribution to assess the performance of the tests in finite samples. An application is presented to illustrate the studied concepts

Local power properties of some asymptotic tests in symmetric linear regression models

In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of symmetric linear regression models. This is a wide class of models which encompasses the t model and several other symmetric distributions with longer-than normal tails. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2011 Elsevier B.V. All rights reserved.

Systematic investigation of a family of gradient-dependent functionals for solids

Eleven density functionals are compared with regard to their performance for the lattice constants of solids. We consider standard functionals, such as the local-density approximation and the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), as well as variations of PBE GGA, such as PBEsol and similar functionals, PBE-type functionals employing a tighter Lieb-Oxford bound, and combinations thereof. On a test set of 60 solids, we perform a system-by-system analysis for selected functionals and a full statistical analysis for all of them. The impact of restoring the gradient expansion and of tightening the Lieb-Oxford bound is discussed, and confronted with previous results obtained from other codes, functionals or test sets. No functional is uniformly good for all investigated systems, but surprisingly, and pleasingly, the simplest possible modifications to PBE turn out to have the most beneficial effect on its performance. The atomization energy of molecules was also considered and on a testing set of six molecules, we found that the PBE functional is clearly the best, the others leading to strong overbinding.

A test of the hypothesis of ecological equivalence in an Australian subtropical rain forest

We tested the hypothesis that tree species in a subtropical rain forest in south-east Queensland are ecologically equivalent and therefore have identical environmental requirements for their regeneration. We assessed the evidence that juveniles of species differed in their distributions in treefall gap microsites and along gradients of light availability, soil pH, soil PO4-P availability and soil NO3-N availability. Pairwise comparisons were made on a subset of the common species selected on the basis that they showed a relatively high level of positive association, and would therefore, a priori, be expected to have similar regeneration requirements. Detailed comparisons between the species failed to demonstrate evidence for species differentiation with respect to their tolerance of the disturbance associated with gap microsites or to the gradient of NO3-N availability. However, species differed markedly in their distributions along the soil pH gradient and along the gradients of light availability and soil PO4-P availability. The overall level of ecological differentiation between the species is high: seven out of the 10 possible species pairings showed evidence for ecological differentiation. Such niche differentiation amongst the juveniles of tree species may play an important role in maintaining the species richness of rain-forest communities.

Testing the link between the latitudinal gradient in species richness and rates of molecular evolution

Numerous hypotheses have been proposed to explain latitudinal gradients in species richness, but all are subject to ongoing debate. Here we examine Rohde's (1978, 1992) hypothesis, which proposes that climatic conditions at low latitudes lead to elevated rates of speciation. This hypothesis predicts that rates of molecular evolution should increase towards lower latitudes, but this prediction has never been tested. We discuss potential links between rates of molecular evolution and latitudinal diversity gradients, and present the first test of latitudinal variation in rates of molecular evolution. Using 45 phylogenetically independent, latitudinally separated pairs of bird species and higher taxa, we compare rates of evolution of two mitochondrial genes and DNA-DNA hybridization distances. We find no support for an effect of latitude on rate of molecular evolution. This result casts doubt on the generality of a key component of Rohde's hypothesis linking climate and speciation.

Actively shielded multi-layer gradient coil designs with improved cooling properties

In standard cylindrical gradient coils consisting of a single layer of wires, a limiting factor in achieving very large magnetic field gradients is the rapid increase in coil resistance with efficiency. This is a particular problem in small-bore scanners, such as those used for MR microscopy. By adopting a multi-layer design in which the coil wires are allowed to spread out into multiple layers wound at increasing radii, a more favourable scaling of resistance with efficiency is achieved, thus allowing the design of more powerful gradient coils with acceptable resistance values. Previously this approach has been applied to the design of unshielded, longitudinal, and transverse gradient coils. Here, the multi-layer approach has been extended to allow the design of actively shielded multi-layer gradient coils, and also to produce coils exhibiting enhanced cooling characteristics. An iterative approach to modelling the steady-state temperature distribution within the coil has also been developed. Results indicate that a good level of screening can be achieved in multi-layer coils, that small versions of such coils can yield higher efficiencies at fixed resistance than conventional two-layer (primary and screen) coils, and that performance improves as the number of layers of increases. Simulations show that by optimising multi-layer coils for cooling it is possible to achieve significantly higher gradient strengths at a fixed maximum operating temperature. A four-layer coil of 8 mm inner diameter has been constructed and used to test the steady-state temperature model. (C) 2003 Elsevier Inc. All rights reserved.

Analysis of genetic diversity of Trypanosoma cruzi: an application of riboprinting and gradient gel electrophoresis methods

Analysis of restriction fragment length polymorphism (RFLP) profiles derived from digestion of polymerase chain reaction (PCR) products of the ribosomal 18S from Trypanosoma cruzi yields a typical `riboprint' profile that can vary intraspecifically. A selection of 21 stocks of T. cruzi and three outgroup taxa: T. rangeli, T. conorhini and Leishmania braziliensis were analysed by riboprinting to assess divergence within and between taxa. T. rangeli, T. conorhini and L. braziliensis could be easily differentiated from each other and from T. cruzi. Phenetic analysis of PCR-RFLP profiles indicated that, with one or two exceptions, stocks of T. cruzi could be broadly partitioned into two groups that formally corresponded to T. cruzi I and T. cruzi II respectively. To test if ribosomal 18S sequences were homogeneous within each taxon, gradient gel electrophoresis methods were employed utilising either chemical or temperature gradients. Upon interpretation of the melting profiles of riboprints and a section of the 18S independently amplified by PCR, there would appear to be at least two divergent 18S types present within T. cruzi. Heterogeneity within copies of the ribosomal 18S within a single genome has therefore been demonstrated and interestingly, this dimorphic arrangement was also present in the outgroup taxa. Presumably the ancestral duplicative event that led to the divergent 18S types preceded that of speciation within this group. These divergent 18S paralogues may have, or had, different functional pressures or rates of molecular evolution. Whether or not these divergent types are equally transcriptionally active throughout the life cycle, remain to be assessed.

Test de sobrecarga acuosa y manometría de alta resolución para valoración de la resistencia al flujo esófago-gástrico en paciente s con acalasia

La manometría convencional es el “gold standard” para diagnosticar trastornos motores del esófago, pero la información que da sobre la repercusión funcional de estas alteraciones es escasa. La manometría de alta resolución permite estudiar con detalle la motilidad esofagogástrica mediante la generación de mapas topográficos de presiones desde la orofaringe hasta el estómago. Hipótesis: Si la generación de mapas topográficos de presiones en el esófago mediante manometría de alta resolución demuestra la resistencia al flujo esofagogástrico. Objetivo: Comprobar si un test con sobrecarga de agua puede mostrar la presencia de resistencia al flujo esofagogástrico en pacientes con acalasia. Método: Estudiamos 2 grupos de pacientes con alteración de la motilidad esofágica. Un grupo de 8 pacientes que cumplen criterios manométricos de acalasia y, como grupo control, 8 pacientes con disfunción del peristaltismo esofágico ( DPE). A cada paciente se le realizó un test de sobrecarga que consistía en la ingesta rápida de 200 ml de agua mientras se registraban las presiones esofágicas. Resultados: Los pacientes con acalasia ingirieron el agua más lentamente que los pacientes con DPE (82± 14 seg vs 34± 6 seg, p&0,05). Mientras la unión gastroesofágica (UGE) permaneció contraída en el grupo de pacientes con acalasia (46,6± 6 mm Hg; p&0,05), permaneció relajada durante el tiempo del ingesta en pacientes con DPE ( 16,6 ± 4,7 mm Hg). La unión esófago-gástrica (UGE) experimentó una migración proximal en pacientes con acalasia de 1,3 ± 0 cm mientras que en el grupo control no migró (0 cm; p&0,05). La ingesta de agua se asoció a un incremento de la presión del esófago distal (2 cm por encima de la UGE) significativamente mayor en los pacientes con acalasia que en los pacientes con DPE (42,2 ± 20 vs 9,5± 7,9 mm Hg respectivamente, p&0,05) lo que produjo un incremento del gradiente de presión esófago-gástrico en pacientes con acalasia (16± 0,9 mmHg) que no se observó en los pacientes con DPE (0,1 ± 0,4 mmHg ; p&0,05). Conclusión: Un test con sobrecarga de agua durante la medición de la topografía y de las presiones esofágicas demuestra obstrucción al flujo esofagogástrico en los pacientes con acalasia. Este test podría contribuir a valorar la repercusión funcional en pacientes con acalasia y podría servir para el seguimiento de pacientes con acalasia tratados.