1,721,345 research outputs found
Discussion of "Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests" by E. del Barrio, J.A. Cuesta-Albertos and C. Matran
No full textOptimal inference for circular variation diminishing experiments with applications to the von-Mises distribution and the Fisher-Efron parabola model
No full textComplete classes and optimal tests for variation diminishing circular distributions are constructed. This is applied to inference for the mean direction of a von Mises distributed r.v. whenever the concentration parameter κ≤½. Similar results are shown for the cardioid and multimodal von-Mises family. Furthermore, our result reinforces the shape of the locally admissible tests for the mean of a bivariate normal r.v. as it was found by Brown & Marden (1992) for the Fisher-Efron parabola model. We find that this test is conditionally optimal whenever the Fisher-information of the experiment is not too large
An unbiased test for the average equivalence problem - the small sample case
No full textBrown et al. (1997, Ann. Statist. 25, 2345-2367) constructed an unbiased test for the bioequivalence problem under some constraints on the level alpha and the sample size. A different construction is presented for the missing cases. Numerical investigations support the conjecture that the rest is unbiased. The suggested test is uniformly more powerful than the standard two one-sided tests procedure. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: primary 62F04; secondary 62P10
An improvement on commonly used tests in bioequivalence assessment
No full textIf equivalence of two treatments has to be proved by an experiment with normally distributed observations and fixed sample size, there are two usual methods. On the one hand, there is the double t test and, on the other hand, a test procedure suggested by Anderson and Hauck, which is uniformly more powerful than the first one but only capable of keeping asymptotically to the nominal level. Based on these two methods a new test is presented, which is uniformly more powerful than the double t test and also keeps the preassigned level
On a problem in pharmaceutical statistics and the iteration of a peculiar nonlinear operator in the upper complex halfplane
No full textIn this paper we discuss the relationship between a well known problem of pharmaceutical statistics, the bioequivalence problem, and a purely geometrical problem, the construction of a certain set in the upper complex halfplane C+. This set has to obey certain peculiar geometric properties due to the restriction of defining the critical region of an unbiased test for the bioequivalance problem. The case for large nominal level alpha and large sample sizes was solved by Brown, Hwang & Munk [2] whereas the existence of such a set for small alpha and sample sizes is still an open problem. We will review in this paper recent developments and highlight some serious practical consequences if such a set would exist. To this end the concept of coherency of a test is introduced. It is shown that unbiased coherent regions do not exist if sample size and level are small
Equivalence and interval testing for Lehmann's alternative
No full textEquivalence and interval tests for Lehmann's alternative that extend the well-known Savage test for one-sided hypotheses are proposed. The proposed tests are shown to be unbiased with a strictly unimodal power function, provided the sample sizes in both treatment groups are equal. By means of a numerical investigation of the bias in the case of unequal sample sizes that are not too far apart, the suggested tests still turn out to provide practicable solutions. Because the computational effort to perform the suggested tests is considerable, tables containing the critical values are displayed to perform these tests easily. A numerical analysis of the power function of the interval test establishes this procedure as a powerful tool for detection of a significantly relevant difference in the small-sample case. In contrast to the case of interval testing, the fact arises that the performance of a powerful equivalence study under Lehmann's alternative requires an extensive amount of data. Because the proposed tests are based on the locally optimal scores under Lehmann's alternative, we cannot improve the suggested equivalence test essentially. Therefore, we also provide the asymptotic version of this test and display tables containing the required numerical values
Testing the goodness of fit of parametric regression models with random Toeplitz forms
No full textWe introduce a class of Toeplitz-band matrices for simple goodness of fit tests for parametric regression models. For a given length r of the band matrix the asymptotic optimal solution is derived. Asymptotic normality of the corresponding test statistic is established under a fixed and random design assumption as well as for linear and non-linear models, respectively. This allows testing at any parametric assumption as well as the computation of confidence intervals for a quadratic measure of discrepancy between the parametric model and the true signal g. Furthermore, the connection between testing the parametric goodness of fit and estimating the error variance is highlighted. As a by-product we obtain a much simpler proof of a result of Hall et al. (1990) concerning the optimality of an estimator for the variance. Our results unify and generalize recent results by Brodeau (1993) and Dette & Munk (1998a,b) in several directions. Extensions to multivariate predictors and unbounded signals are discussed. A simulation study shows that a simple jacknife correction of the proposed test statistics leads to reasonable finite sample approximations
A note on unbiased testing for the equivalence problem - another christmas tree
No full textBrown et al. (1998) recently constructed an unbiased test for the bioequivalence problem. We give another construction which shows that this test is not UMPU. (C) 1999 Elsevier Science B.V. All rights reserved
Discussion of "Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests" by E. del Barrio, J.A. Cuesta-Albertos and C. Matran
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