Generalised score and Wald tests.
Generalization of discrimination-rate theorems of Chernoff and Stein
Generalized F tests and selective generalized F tests for orthogonal and associated mixed models
The statistics of generalized F tests are quotients of linear combinations of independent chi-squares. Given a parameter, θ, for which we have a quadratic unbiased estimator, θ̃, the test statistic, for the hypothesis of nullity of that parameter, is the quotient of the positive part by the negative part of such estimator. Using generalized polar coordinates it is possible to obtain selective generalized F tests which are especially powerful for selected families of alternatives. We build both classes...
Generalized F tests in models with random perturbations: the gamma case
Generalized F tests were introduced for linear models by Michalski and Zmyślony (1996, 1999). When the observations are taken in not perfectly standardized conditions the F tests have generalized F distributions with random non-centrality parameters, see Nunes and Mexia (2006). We now study the case of nearly normal perturbations leading to Gamma distributed non-centrality parameters.
Geometry, statistics and decision making in gene therapy.
Global information in statistical experiments and consistency of likelihood-based estimates and tests
In the framework of standard model of asymptotic statistics we introduce a global information in the statistical experiment about the occurrence of the true parameter in a given set. Basic properties of this information are established, including relations to the Kullback and Fisher information. Its applicability in point estimation and testing statistical hypotheses is demonstrated.
Goodness-of-fit test for long range dependent processes
In this paper, we make use of the information measure introduced by Mokkadem (1997) for building a goodness-of-fit test for long-range dependent processes. Our test statistic is performed in the frequency domain and writes as a non linear functional of the normalized periodogram. We establish the asymptotic distribution of our statistic under the null hypothesis. Under specific alternative hypotheses, we prove that the power converges to one. The performance of our test procedure is illustrated...
Goodness-of-fit test for long range dependent processes
In this paper, we make use of the information measure introduced by Mokkadem (1997) for building a goodness-of-fit test for long-range dependent processes. Our test statistic is performed in the frequency domain and writes as a non linear functional of the normalized periodogram. We establish the asymptotic distribution of our statistic under the null hypothesis. Under specific alternative hypotheses, we prove that the power converges to one. The performance of our test procedure is illustrated...
Goodness-of-fit test for the family of logistic distributions.
Chi-squared goodness-of-fit test for the family of logistic distributions id proposed. Different methods of estimation of the unknown parameters θ of the family are compared. The problem of homogeneity is considered.
Goodness-of-fit tests based on -divergence
In this paper a new family of statistics based on -divergence for testing goodness-of-fit under composite null hypotheses are considered. The asymptotic distribution of this test is obtained when the unspecified parameters are estimated by maximum likelihood as well as minimum -divergence.
Goodness-of-fit tests in long-range dependent processes under fixed alternatives
In a recent paper Fay and Philippe [ESAIM: PS 6 (2002) 239–258] proposed a goodness-of-fit test for long-range dependent processes which uses the logarithmic contrast as information measure. These authors established asymptotic normality under the null hypothesis and local alternatives. In the present note we extend these results and show that the corresponding test statistic is also normally distributed under fixed alternatives.
Goodness-of-fit tests using characterizations of continuous distributions
Using characterization conditions of continuous distributions in terms of moments of order statistics and moments of record values we present new goodness-of-fit techniques.