Quartz recrystallization regimes, c-axis texture transitions and fluid inclusion reequilibration in a prograde greenschist to amphibolite facies mylonite zone (Ribeira Shear Zone, SE Brazil)

The crystal-plastic behavior of quartz mylonites from the Ribeira Shear Zone (SE Brazil), a major strike-slip structure that was active during a prograde metamorphic phase related to the Neoproterozoic Brasiliano-Pan African Orogeny, was investigated using a multi-method approach. Geothermobarometry results indicate deformational conditions ranging from similar to 300 to similar to 630 degrees C and 500-700 MPa. A strong correlation between mapped metamorphic zones and a dominance of different dynamic recrystallization mechanisms of quartz occurs within the mylonite zone. Bulging recrystallization (BLG) dominates within the chlorite zone between 300 and 410 degrees C, subgrain rotation recrystallization (SGR) operates within the biotite zone from 410 to 520 degrees C, and grain boundary migration recrystallization (GBM) dominates in the garnet zone above 520 degrees C. The development of quartz c-axis textures is mainly governed by temperature and dynamic recrystallization mechanisms. Textures from BLG zone mylonites are characterized by maxima around Z; SGR zone mylonites display single girdles or asymmetric type I crossed girdles; and GBM zone mylonites comprise maxima around Y and intermediate between X and Z. The scarcity or absence of water-bearing fluid inclusions in quartz mylonites from the SGR and GBM zones, which are dominated by carbonic inclusions, suggests water-deficient conditions, whereas BLG zone mylonites are dominated by water-bearing inclusions. This evidence indicates that water was available in the protoliths but has been eliminated with increasing deformation and deformation temperature. No effect of the water content variation on the quartz microstructural and recrystallized grain size evolution was detected, and little influence on c-axis texture development was observed. Most of the fluid inclusion densities were reequilibrated during the shear zone exhumation history, recording a decompression in the range of 300-500 MPa, while microstructural reequilibration effects related to the prograde metamorphism are largely preserved. Fluid inclusion microstructures and densities from two SGR zone samples preserved evidence for a near isothermal compression within the interior of the Ribeira Shear Zone during the prograde metamorphism. (C) 2009 Elsevier B.V. All rights reserved.

Cambrian mafic to felsic magmatism and its connections with transcurrent shear zones of the Borborema Province (NE Brazil): Implications for the late assembly of the West Gondwana

New U-Pb (SHRIMP) and (40)Ar/(39)Ar isotopic data of igneous rocks and mylonites of the Borborema Province (NE Brazil) show that a wide range of tectonothermal events affected the province during the transition from the Precambrian to the Cambrian. Concordant zircon U-Pb data constrained the crystallization age of mafic stocks, mafic to felsic dikes and granite batholiths between 548 and 533 Ma. These bodies were emplaced in a regional strain field combining extension and dextral shearing. The ductile shear deformation overprinted an older basement fabric to develop a low- to medium metamorphic grade vertical mylonite belt that cut the province in the E-W direction. Magnetic fabrics of the Cambrian batholiths determined by anisotropy of magnetic susceptibility are consistent with syntectonic emplacement. The magmatic pulses and shear deformation would have supplied enough heat to reset the synkinematic micas of mylonites to yield (40)Ar/(39)Ar plateau cooling ages between ca. 550 and 510 Ma. These results provide evidence that emplacement of Early Cambrian mafic and felsic magmas were accompanied by regional-scale shear deformations, probably in the consequence of late collisions along the West Gondwana margin. (C) 2010 Published by Elsevier B.V.

Fabrics of pre- and syntectonic granite plutons and chronology of shear zones in the Eastern Borborema Province, NE Brazil

We used the fabrics of two granite plutons and U/Pb (SHRIMP) zircon ages to constrain the tectonic evolution of the E-trending Patos shear zone (Borborema Province, NE Brazil). The pre-tectonic Teixeira batholith consists of an amphibole leucogranite locally with aegirine-augite. Zircons from a syenogranite yielded crystallization ages of 591 +/- 5 Ma. The batholith fabrics were determined by anisotropy of magnetic susceptibility (AMS) and mineral shape preferred orientation. The fabrics support pre-transcurrent batholith emplacement, as evidenced by: (i) magmatic/magnetic fabrics in low susceptibility (<0.35 mSI) leucogranites highly discordant to the regional host rock structure, and (ii) concordant magnetic fabrics restricted to high susceptibility (>1 mSI) corridors connected to shear zones branching off from Patos. One of these satellite shear zones controlled the syntectonic emplacement of the Serra Redonda pluton, which yields a crystallization age of 576 +/- 3 Ma. This late shearing event marks the peak regional deformation that, south of Patos, was coupled to crustal shortening nearly perpendicular to the shear belt. The chronology of the deformational events indicates that the major shear zones of the eastern Borborema are late structures active after the crustal blocks amalgamated. (C) 2007 Elsevier Ltd. All rights reserved.

Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

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.

Signed likelihood ratio tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders regression model is becoming increasingly popular in lifetime analyses and reliability studies. In this model, the signed likelihood ratio statistic provides the basis for testing inference and construction of confidence limits for a single parameter of interest. We focus on the small sample case, where the standard normal distribution gives a poor approximation to the true distribution of the statistic. We derive three adjusted signed likelihood ratio statistics that lead to very accurate inference even for very small samples. Two empirical applications are presented. (C) 2010 Elsevier B.V. All rights reserved.

Comparing diagnostic tests with missing data

When missing data occur in studies designed to compare the accuracy of diagnostic tests, a common, though naive, practice is to base the comparison of sensitivity, specificity, as well as of positive and negative predictive values on some subset of the data that fits into methods implemented in standard statistical packages. Such methods are usually valid only under the strong missing completely at random (MCAR) assumption and may generate biased and less precise estimates. We review some models that use the dependence structure of the completely observed cases to incorporate the information of the partially categorized observations into the analysis and show how they may be fitted via a two-stage hybrid process involving maximum likelihood in the first stage and weighted least squares in the second. We indicate how computational subroutines written in R may be used to fit the proposed models and illustrate the different analysis strategies with observational data collected to compare the accuracy of three distinct non-invasive diagnostic methods for endometriosis. The results indicate that even when the MCAR assumption is plausible, the naive partial analyses should be avoided.

Small-Sample Corrections for Score Tests in Birnbaum-Saunders Regressions

In this article, we deal with the issue of performing accurate small-sample inference in the Birnbaum-Saunders regression model, which can be useful for modeling lifetime or reliability data. We derive a Bartlett-type correction for the score test and numerically compare the corrected test with the usual score test and some other competitors.

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

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.

Modifications and Alternatives to the Tests of Levene and Brown & Forsythe for Equality of Variances and Means

The usual tests to compare variances and means (e. g. Bartlett`s test and F-test) assume that the sample comes from a normal distribution. In addition, the test for equality of means requires the assumption of homogeneity of variances. In some situation those assumptions are not satisfied, hence we may face problems like excessive size and low power. In this paper, we describe two tests, namely the Levene`s test for equality of variances, which is robust under nonnormality; and the Brown and Forsythe`s test for equality of means. We also present some modifications of the Levene`s test and Brown and Forsythe`s test, proposed by different authors. We analyzed and applied one modified form of Brown and Forsythe`s test to a real data set. This test is a robust alternative under nonnormality, heteroscedasticity and also when the data set has influential observations. The equality of variance can be well tested by Levene`s test with centering at the sample median.

Some restriction tests in a new class of regression models for proportions

The main purpose of this work is to study the behaviour of Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-32] adjusted likelihood ratio statistic in testing simple hypothesis in a new class of regression models proposed here. The proposed class of regression models considers Dirichlet distributed observations, and the parameters that index the Dirichlet distributions are related to covariates and unknown regression coefficients. This class is useful for modelling data consisting of multivariate positive observations summing to one and generalizes the beta regression model described in Vasconcellos and Cribari-Neto [Vasconcellos, K.L.P., Cribari-Neto, F., 2005. Improved maximum likelihood estimation in a new class of beta regression models. Brazilian journal of Probability and Statistics 19,13-31]. We show that, for our model, Skovgaard`s adjusted likelihood ratio statistics have a simple compact form that can be easily implemented in standard statistical software. The adjusted statistic is approximately chi-squared distributed with a high degree of accuracy. Some numerical simulations show that the modified test is more reliable in finite samples than the usual likelihood ratio procedure. An empirical application is also presented and discussed. (C) 2009 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.

In vitro tests to establish LC(50) and discriminating concentrations for fipronil against Rhipicephalus (Boophilus) microplus (Acari: Ixodidae) and their standardization

Laboratory test was carried out on larvae and adults of the cattle tick, Rhipicephalus (Boophilus) microplus, to determine fipronil toxicity. Adult immersion test (AIT, N = 26), larval immersion test (LIT, N = 71) and larval packet test (LPT, N = 41) were standardized using susceptible strain (Mozo). Dose-response curves were compared with a fipronil resistant strain. Four variables were analyzed from AIT results: mortality, weight of eggs on day 7 and on day 14, index of fertility, and index of fecundity. For larval test, dose mortality curves were analyzed. In spite of the high LC(50) variability, all variables determined for AIT were appropriate to discriminate both strains. AIT and LIT had more sensitivity than LPT, with larger resistance factors. It was used two times LC(99.9) as discriminating doses (DCs) following FAO suggestion. For mortality by AIT, LIT and LPT the DCs were estimated: 4.98 ppm, 7.64 ppm and 2365.8 ppm, respectively, for Mozo strain. DCs mortality values estimated for resistant strain by AIT, LIT and LPT were: 6.96 x 10(5) ppm, 343.26 ppm and 5.7 x 10(3) ppm, respectively and their respective resistant factors were: 202.4, 5.36 and 1.52. Protocols for AIT, LIT and LPT have been presented in this paper. (C) 2009 Elsevier B.V. All rights reserved.