182 research outputs found
Improved Likelihood Inference in Birnbaum-Saunders Regressions
The Birnbaum-Saunders regression model is commonly used in reliability
studies. We address the issue of performing inference in this class of models
when the number of observations is small. We show that the likelihood ratio
test tends to be liberal when the sample size is small, and we obtain a
correction factor which reduces the size distortion of the test. The correction
makes the error rate of he test vanish faster as the sample size increases. The
numerical results show that the modified test is more reliable in finite
samples than the usual likelihood ratio test. We also present an empirical
application.Comment: 17 pages, 1 figur
Small-sample corrections for score tests in Birnbaum-Saunders regressions
In this paper 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, the likelihood ratio test and its Bartlett-corrected version. Our
simulation results suggest that the corrected test we propose is more reliable
than the other tests.Comment: To appear in the Communications in Statistics - Theory and Methods,
http://www.informaworld.com/smpp/title~content=t71359723
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 and
under a sequence of Pitman alternatives, for the nonnull 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 an
empirical application.Comment: Paper submitted for publication, with 13 pages and 1 figur
A log-Birnbaum-Saunders Regression Model with Asymmetric Errors
The paper by Leiva et al. (2010) introduced a skewed version of the
sinh-normal distribution, discussed some of its properties and characterized an
extension of the Birnbaum-Saunders distribution associated with this
distribution. In this paper, we introduce a skewed log-Birnbaum-Saunders
regression model based on the skewed sinh-normal distribution. Some influence
methods, such as the local influence and generalized leverage are presented.
Additionally, we derived the normal curvatures of local influence under some
perturbation schemes. An empirical application to a real data set is presented
in order to illustrate the usefulness of the proposed model.Comment: Submitted for publicatio
Birnbaum-Saunders nonlinear regression models
We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear
regression models potentially useful in lifetime data analysis. The class
generalizes the regression model described by Rieck and Nedelman [1991, A
log-linear model for the Birnbaum-Saunders distribution, Technometrics, 33,
51-60]. We discuss maximum likelihood estimation for the parameters of the
model, and derive closed-form expressions for the second-order biases of these
estimates. Our formulae are easily computed as ordinary linear regressions and
are then used to define bias corrected maximum likelihood estimates. Some
simulation results show that the bias correction scheme yields nearly unbiased
estimates without increasing the mean squared errors. We also give an
application to a real fatigue data set
Local power of the LR, Wald, score and gradient tests in dispersion models
We derive asymptotic expansions up to order 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 it is shown that there
is no uniform superiority of one test with respect to the others 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.Comment: Submitted for publicatio
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