DSpace Collection:
http://hdl.handle.net/10316/15544
Thu, 19 Sep 2019 02:55:18 GMT2019-09-19T02:55:18ZOn the automatic selection of the tuning parameter appearing in certain families of goodness-of-fit tests
http://hdl.handle.net/10316/87197
Title: On the automatic selection of the tuning parameter appearing in certain families of goodness-of-fit tests
Authors: Tenreiro, Carlos
Abstract: The situation, common in the current literature, is that of a whole family of location-scale/scale invariant test statistics, indexed by a parameter $\lambda\in\Lambda$, is available to test the goodness of fit of $F$, the underlying distribution function of a set of independent real-valued random variables, to a location-scale/scale family of distribution functions. The power properties of the tests associated with the different statistics usually depend on the parameter $\lambda$, called the ``tuning parameter'', which is the reason that its choice is crucial to obtain a performing test procedure. In this paper, we address the automatic selection of the tuning parameter when $\Lambda$ is finite, as well as the calibration of the associated goodness-of-fit test procedure. Examples of existing and new tuning parameter selectors are discussed, and the methodology presented of combining different test statistics into a single test procedure is applied to well known families of test statistics for normality and exponentiality. A simulation study is carried out to access the power of the different tests under consideration, and to
compare them with the fixed tuning parameter procedure, usually recommended in the literature.Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10316/871972019-01-01T00:00:00ZITERATED FAILURE RATE MONOTONICITY AND ORDERING RELATIONS WITHIN GAMMA AND WEIBULL DISTRIBUTIONS
http://hdl.handle.net/10316/84950
Title: ITERATED FAILURE RATE MONOTONICITY AND ORDERING RELATIONS WITHIN GAMMA AND WEIBULL DISTRIBUTIONS
Authors: Arab, Idir; Oliveira, Paulo
Abstract: Stochastic ordering of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings, by iteratively reassigning tail-weights. The actual verification of stochastic orderings is not simple, as this depends on inverting distribution functions for which there may be no explicit expression. The iterative definition of distributions, of course, contributes to make that verification even harder. We have a look at the stochastic ordering, introducing a method that allows for explicit usage, applying it to the Gamma and Weibull distributions, giving a complete description of the order of relations within each of these families.Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10316/849502018-01-01T00:00:00ZASYMPTOTIC RESULTS FOR CERTAIN WEAK DEPENDENT VARIABLES
http://hdl.handle.net/10316/84943
Title: ASYMPTOTIC RESULTS FOR CERTAIN WEAK DEPENDENT VARIABLES
Authors: Arab, Idir; Oliveira, Paulo
Abstract: We consider a special class of weak dependent random variables with control on covariances
of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated
variables and a few other classes of weakly dependent structures. We prove the Strong Law of Large
Numbers with the characterization of convergence rates which is almost optimal, in the sense that it
is arbitrarily close to the optimal rate for independent variables. Moreover, we prove an inequality
comparing the joint distributions with the product distributions of the margins, similar to the well
known Newman's inequality for characteristic functions of associated variables. As a consequence, we
prove the Central Limit Theorem together with its functional counterpart, and also the convergence
of the empirical process for this class of weak dependent variables.Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10316/849432018-01-01T00:00:00ZOn the choice of the smoothing parameter for the BHEP goodness-of-fit test
http://hdl.handle.net/10316/80929
Title: On the choice of the smoothing parameter for the BHEP goodness-of-fit test
Authors: Tenreiro, Carlos
Abstract: The BHEP (Baringhaus--Henze--Epps--Pulley) test for assessing univariate and multivariate normality has shown itself to be a relevant test procedure, recommended in some recent comparative studies. It is well known that the finite sample behaviour of the BHEP goodness-of-fit test strongly depends on the choice of a smoothing parameter $h$. A theoretical and finite sample based description of the role played by the smoothing parameter in the detection of departures from the null hypothesis of normality is given. Additionally, the results of a Monte Carlo study are reported in order to propose an easy-to-use rule for choosing $h$. In the important multivariate case, and contrary to the usual choice of $h$, the BHEP test with the proposed smoothing parameter presents
a comparatively good performance against a wide range of alternative distributions. In practice, if no relevant information about the tail of the alternatives is available, the use of this new bandwidth is strongly recommended. Otherwise, new choices of $h$ which are suitable for short tailed and long tailed alternative distributions are also proposed.Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/809292009-01-01T00:00:00Z