Geochronological data from the Faxinal coal succession, southern Parana Basin, Brazil: A preliminary approach combining radiometric U-Pb dating and palynostratigraphy

A radiometric zircon age of 285.4 +/- 8.6 Ma (IDTIMS U-Pb) is reported from a tonstein layer interbedded with coal seams in the Faxinal coalfield, Rio Grande do Sul, Brazil. Calibration of palynostratigraphic data with the absolute age shows that the coal depositional interval in the southern Parana Basin is constrained to the Sakmarian. Consequently, the basal Gondwana sequence in the southern part of the basin should lie at the Carboniferous-Permian boundary, not within the Sakmarian as previously considered. The new results are significant for correlations between the Parana Basin and the Argentinian Paganzo Basin (302 +/- 6 Ma and 288 +/- 7 Ma) and with the Karoo Basin, specifically with the top of the Dwyka Tillite (302 +/- 3 Ma and 299.2 +/- 3.2 Ma) and the lowermost Ecca Group (288 +/- 3 Ma and 289.6 +/- 3.8 Ma). The evidence signifies widespread latest Carboniferous volcanic activity in western Gondwana. (C) 2007 Elsevier Ltd. 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.