Chemical process to separate iron oxides particles in pottery sample for EPR dating

Ancient potteries usually are made of the local clay material, which contains relatively high concentration of iron. The powdered samples are usually quite black, due to magnetite, and, although they can be used for thermoluminescene (TL) dating, it is easiest to obtain better TL reading when clearest natural or pre-treated sample is used. For electron paramagnetic resonance (EPR) measurements, the huge signal due to iron spin-spin interaction, promotes an intense interference overlapping any other signal in this range. Sample dating is obtained by dividing the radiation dose, determined by the concentration of paramagnetic species generated by irradiation, by the natural dose so as a consequence, EPR dating cannot be used, since iron signal do not depend on radiation dose. In some cases, the density separation method using hydrated solution of sodium polytungstate [Na(G)(H(2)W(12)O(40))center dot H(2)O] becomes useful. However, the sodium polytungstate is very expensive in Brazil: hence an alternative method for eliminating this interference is proposed. A chemical process to eliminate about 90% of magnetite was developed. A sample of powdered ancient pottery was treated in a mixture (3:1:1) of HCI, HNO(3) and H(2)O(2) for 4 h. After that, it was washed several times in distilled water to remove all acid matrixes. The original black sample becomes somewhat clearer. The resulting material was analyzed by plasma mass spectrometry (ICP-MS), with the result that the iron content is reduced by a factor of about 9. In EPR measurements a non-treated natural ceramic sample shows a broad spin-spin interaction signal, the chemically treated sample presents a narrow signal in g= 2.00 region, possibly due to a radical of (SiO(3))(3-), mixed with signal of remaining iron [M. lkeya, New Applications of Electron Spin Resonance, World Scientific, Singapore, 1993, p. 285]. This signal increases in intensity under -gamma-irradiation. However, still due to iron influence, the additive method yielded too old age-value. Since annealing at 300 degrees C, Toyoda and Ikeya IS. Toyoda, M. Ikeya, Geochem. J. 25 (1991) 427-445] states that E `(1)-signal with maximum intensity is obtained, while annealing at 400 degrees C E`(1)-signal is completely eliminated, the subtraction of the second one from 300 degrees C heat-treated sample isolate E`(1)-like signal. Since this is radiation dose-dependent, we show that now EPR dating becomes possible. (C) 2008 Elsevier B.V. All rights reserved.

TL, EPR and optical absorption in natural grossular crystal

Grossular is one of six members of silicate Garnet group. Two samples GI and GII have been investigated concerning their luminescence thermally stimulated (TL). EPR and optical absorption and the measurements were carried out to find out whether or not same point defects are responsible for all three properties. Although X-rays diffraction analysis has shown that both GI and GII have practically the same crystal structure of a standard grossular crystal, they presented different behavior in many aspects. The TL glow curve shape, TL response to radiation dose, the effect of annealing at high temperatures before irradiation, the dependence of UV bleaching parameters on peak temperature, all of them differ going from GI to GII. The EPR signals around g = 2.0 as well as at g = 4.3 and 6.0 have much larger intensity in GI than in GII. Very high temperature (> 800 degrees C annealing causes large increase in the bulk background absorption in GI, however, only very little in GII. In the cases of EPR and optical absorption, the difference in their behavior can be attributed to Fe3+ ions; however, in the TL case one cannot and the cause was not found as yet. (C) 2008 Elsevier B.V. All rights reserved.

Deviance residuals in generalised log-gamma regression models with censored observations

In this article, we compare three residuals based on the deviance component in generalised log-gamma regression models with censored observations. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. For all cases studied, the empirical distributions of the proposed residuals are in general symmetric around zero, but only a martingale-type residual presented negligible kurtosis for the majority of the cases studied. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for the martingale-type residual in generalised log-gamma regression models with censored data. A lifetime data set is analysed under log-gamma regression models and a model checking based on the martingale-type residual is performed.

Improved likelihood inference for the shape parameter in Weibull regression

We obtain adjustments to the profile likelihood function in Weibull regression models with and without censoring. Specifically, we consider two different modified profile likelihoods: (i) the one proposed by Cox and Reid [Cox, D.R. and Reid, N., 1987, Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B, 49, 1-39.], and (ii) an approximation to the one proposed by Barndorff-Nielsen [Barndorff-Nielsen, O.E., 1983, On a formula for the distribution of the maximum likelihood estimator. Biometrika, 70, 343-365.], the approximation having been obtained using the results by Fraser and Reid [Fraser, D.A.S. and Reid, N., 1995, Ancillaries and third-order significance. Utilitas Mathematica, 47, 33-53.] and by Fraser et al. [Fraser, D.A.S., Reid, N. and Wu, J., 1999, A simple formula for tail probabilities for frequentist and Bayesian inference. Biometrika, 86, 655-661.]. We focus on point estimation and likelihood ratio tests on the shape parameter in the class of Weibull regression models. We derive some distributional properties of the different maximum likelihood estimators and likelihood ratio tests. The numerical evidence presented in the paper favors the approximation to Barndorff-Nielsen`s adjustment.

Measuring time series predictability using support vector regression

Most studies involving statistical time series analysis rely on assumptions of linearity, which by its simplicity facilitates parameter interpretation and estimation. However, the linearity assumption may be too restrictive for many practical applications. The implementation of nonlinear models in time series analysis involves the estimation of a large set of parameters, frequently leading to overfitting problems. In this article, a predictability coefficient is estimated using a combination of nonlinear autoregressive models and the use of support vector regression in this model is explored. We illustrate the usefulness and interpretability of results by using electroencephalographic records of an epileptic patient.

On beta regression residuals

We propose two new residuals for the class of beta regression models, and numerically evaluate their behaviour relative to the residuals proposed by Ferrari and Cribari-Neto. Monte Carlo simulation results and empirical applications using real and simulated data are provided. The results favour one of the residuals we propose.

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.

Improved likelihood inference in beta regression

We consider the issue of performing accurate small-sample likelihood-based inference in beta regression models, which are useful for modelling continuous proportions that are affected by independent variables. We derive small-sample adjustments to the likelihood ratio statistic in this class of models. The adjusted statistics can be easily implemented from standard statistical software. We present Monte Carlo simulations showing that inference based on the adjusted statistics we propose is much more reliable than that based on the usual likelihood ratio statistic. A real data example is presented.

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

Bayesian estimation of regression parameters in elliptical measurement error models

The main object of this paper is to discuss the Bayes estimation of the regression coefficients in the elliptically distributed simple regression model with measurement errors. The posterior distribution for the line parameters is obtained in a closed form, considering the following: the ratio of the error variances is known, informative prior distribution for the error variance, and non-informative prior distributions for the regression coefficients and for the incidental parameters. We proved that the posterior distribution of the regression coefficients has at most two real modes. Situations with a single mode are more likely than those with two modes, especially in large samples. The precision of the modal estimators is studied by deriving the Hessian matrix, which although complicated can be computed numerically. The posterior mean is estimated by using the Gibbs sampling algorithm and approximations by normal distributions. The results are applied to a real data set and connections with results in the literature are reported. (C) 2011 Elsevier B.V. All rights reserved.

Prediction in Multilevel Logistic Regression

The purpose of this article is to present a new method to predict the response variable of an observation in a new cluster for a multilevel logistic regression. The central idea is based on the empirical best estimator for the random effect. Two estimation methods for multilevel model are compared: penalized quasi-likelihood and Gauss-Hermite quadrature. The performance measures for the prediction of the probability for a new cluster observation of the multilevel logistic model in comparison with the usual logistic model are examined through simulations and an application.

Framework for Skew-Probit Links in Binary Regression

We review several asymmetrical links for binary regression models and present a unified approach for two skew-probit links proposed in the literature. Moreover, under skew-probit link, conditions for the existence of the ML estimators and the posterior distribution under improper priors are established. The framework proposed here considers two sets of latent variables which are helpful to implement the Bayesian MCMC approach. A simulation study to criteria for models comparison is conducted and two applications are made. Using different Bayesian criteria we show that, for these data sets, the skew-probit links are better than alternative links proposed in the literature.

Diagnostic tools in beta regression with varying dispersion

We consider the issue of performing residual and local influence analyses in beta regression models with varying dispersion, which are useful for modelling random variables that assume values in the standard unit interval. In such models, both the mean and the dispersion depend upon independent variables. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. An application using real data is presented and discussed.