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.

Reliability Nonparametric Bayesian Estimation in Parallel Systems

Relevant results for (sub-)distribution functions related to parallel systems are discussed. The reverse hazard rate is defined using the product integral. Consequently, the restriction of absolute continuity for the involved distributions can be relaxed. The only restriction is that the sets of discontinuity points of the parallel distributions have to be disjointed. Nonparametric Bayesian estimators of all survival (sub-)distribution functions are derived. Dual to the series systems that use minimum life times as observations, the parallel systems record the maximum life times. Dirichlet multivariate processes forming a class of prior distributions are considered for the nonparametric Bayesian estimation of the component distribution functions, and the system reliability. For illustration, two striking numerical examples are presented.

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.

Saliva flow rate, buffer capacity, and pH of autistic individuals

The objective of the study was to evaluate saliva flow rate, buffer capacity, pH levels, and dental caries experience (DCE) in autistic individuals, comparing the results with a control group (CG). The study was performed on 25 noninstitutionalized autistic boys, divided in two groups. G1 composed of ten children, ages 3-8. G2 composed of 15 adolescents ages 9-13. The CG was composed of 25 healthy boys, randomly selected and also divided in two groups: CG3 composed of 14 children ages 4-8, and CG4 composed of 11 adolescents ages 9-14. Whole saliva was collected under slight suction, and pH and buffer capacity were determined using a digital pHmeter. Buffer capacity was measured by titration using 0.01 N HCl, and the flow rate expressed in ml/min, and the DCE was expressed by decayed, missing, and filled teeth (permanent dentition [DMFT] and primary dentition [dmft]). Data were plotted and submitted to nonparametric (Kruskal-Wallis) and parametric (Student`s t test) statistical tests with a significance level less than 0.05. When comparing G1 and CG3, groups did not differ in flow rate, pH levels, buffer capacity, or DMFT. Groups G2 and CG4 differ significantly in pH (p = 0.007) and pHi = 7.0 (p = 0.001), with lower scores for G2. In autistic individuals aged 3-8 and 9-13, medicated or not, there was no significant statistical difference in flow rate, pH, and buffer capacity. The comparison of DCE among autistic children and CG children with deciduous (dmft) and mixed/permanent decayed, missing, and filled teeth (DMFT) did not show statistical difference (p = 0.743). Data suggest that autistic individuals have neither a higher flow rate nor a better buffer capacity. Similar DCE was observed in both groups studied.

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.

Machine vision for the automatic classification of images acquired from Non-destructive tests

This project is based on Artificial Intelligence (A.I) and Digital Image processing (I.P) for automatic condition monitoring of sleepers in the railway track. Rail inspection is a very important task in railway maintenance for traffic safety issues and in preventing dangerous situations. Monitoring railway track infrastructure is an important aspect in which the periodical inspection of rail rolling plane is required.Up to the present days the inspection of the railroad is operated manually by trained personnel. A human operator walks along the railway track searching for sleeper anomalies. This monitoring way is not more acceptable for its slowness and subjectivity. Hence, it is desired to automate such intuitive human skills for the development of more robust and reliable testing methods. Images of wooden sleepers have been used as data for my project. The aim of this project is to present a vision based technique for inspecting railway sleepers (wooden planks under the railway track) by automatic interpretation of Non Destructive Test (NDT) data using A.I. techniques in determining the results of inspection.