Testing uniformity on high-dimensional spheres against monotone rotationally symmetric alternatives

We consider the problem of testing uniformity on high-dimensional unit spheres. We are primarily interested in non-null issues. We show that rotationally symmetric alternatives lead to two Local Asymptotic Normality (LAN) structures. The first one is for fixed modal location $\theta$ and allows to derive locally asymptotically most powerful tests under specified $\theta$. The second one, that addresses the Fisher-von Mises-Langevin (FvML) case, relates to the unspecified-$\theta$ problem and shows that the high-dimensional Rayleigh test is locally asymptotically most powerful invariant. Under mild assumptions, we derive the asymptotic non-null distribution of this test, which allows to extend away from the FvML case the asymptotic powers obtained there from Le Cam's third lemma. Throughout, we allow the dimension $p$ to go to infinity in an arbitrary way as a function of the sample size $n$. Some of our results also strengthen the local optimality properties of the Rayleigh test in low dimensions. We perform a Monte Carlo study to illustrate our asymptotic results. Finally, we treat an application related to testing for sphericity in high dimensions

East Bay Coalition for the Homeless: Branding Study and Marketing Strategy

There are a number of potential positioning strategies. The two which make the most sense for the EBCH are to “position the EBCH away from others in the category” and to “position the EBCH as unique.” These strategies have the advantage of setting the EBCH apart from the other organizations that address homelessness. Occupying its own “position” in the minds of potential and current donors is not only an effective communications/marketing strategy but also a less costly one because it avoids head-to-head competition and comparisons

Fludarabine, cytarabine, granulocyte colony-stimulating factor, and idarubicin with gemtuzumab ozogamicin improves event-free survival in younger patients with newly diagnosed aml and overall survival in patients with npm1 and flt3 mutations

Purpose To determine the optimal induction chemotherapy regimen for younger adults with newly diagnosed AML without known adverse risk cytogenetics. Patients and Methods One thousand thirty-three patients were randomly assigned to intensified (fludarabine, cytarabine, granulocyte colony-stimulating factor, and idarubicin [FLAG-Ida]) or standard (daunorubicin and Ara-C [DA]) induction chemotherapy, with one or two doses of gemtuzumab ozogamicin (GO). The primary end point was overall survival (OS). Results There was no difference in remission rate after two courses between FLAG-Ida + GO and DA + GO (complete remission [CR] + CR with incomplete hematologic recovery 93% v 91%) or in day 60 mortality (4.3% v 4.6%). There was no difference in OS (66% v 63%; P = .41); however, the risk of relapse was lower with FLAG-Ida + GO (24% v 41%; P < .001) and 3-year event-free survival was higher (57% v 45%; P < .001). In patients with an NPM1 mutation (30%), 3-year OS was significantly higher with FLAG-Ida + GO (82% v 64%; P = .005). NPM1 measurable residual disease (MRD) clearance was also greater, with 88% versus 77% becoming MRD-negative in peripheral blood after cycle 2 (P = .02). Three-year OS was also higher in patients with a FLT3 mutation (64% v 54%; P = .047). Fewer transplants were performed in patients receiving FLAG-Ida + GO (238 v 278; P = .02). There was no difference in outcome according to the number of GO doses, although NPM1 MRD clearance was higher with two doses in the DA arm. Patients with core binding factor AML treated with DA and one dose of GO had a 3-year OS of 96% with no survival benefit from FLAG-Ida + GO. Conclusion Overall, FLAG-Ida + GO significantly reduced relapse without improving OS. However, exploratory analyses show that patients with NPM1 and FLT3 mutations had substantial improvements in OS. By contrast, in patients with core binding factor AML, outcomes were excellent with DA + GO with no FLAG-Ida benefit

Testing uniformity against rotationally symmetric alternatives on high-dimensional spheres

Dans cette thèse, nous nous intéressons au problème de tester en grande dimension l'uniformité sur la sphère-unité $S^{p_n-1}$ (la dimension des observations, $p_n$, dépend de leur nombre, $n$, et être en grande dimension signifie que $p_n$ tend vers l'infini en même temps que $n$). Nous nous restreignons dans un premier temps à des contre-hypothèses ``monotones'' de densité croissante le long d'une direction ${\pmb \theta}_n\in S^{p_n-1}$ et dépendant d'un paramètre de concentration $\kappa_n>0$. Nous commençons par identifier le taux $\kappa_n$ auquel ces contre-hypothèses sont contiguës à l'uniformité ;nous montrons ensuite grâce à des résultats de normalité locale asymptotique, que le test d'uniformité le plus classique, le test de Rayleigh, n'est pas optimal quand ${\pmb \theta}_n$ est connu mais qu'il le devient à $p$ fixé et dans le cas FvML en grande dimension quand ${\pmb \theta}_n$ est inconnu.Dans un second temps, nous considérons des contre-hypothèses ``axiales'', attribuant la même probabilité à des points diamétralement opposés. Elles dépendent aussi d'un paramètre de position ${\pmb \theta}_n\in S^{p_n-1}$ et d'un paramètre de concentration $\kappa_n\in\R$. Le taux de contiguïté s'avère ici plus élevé et suggère un problème plus difficile que dans le cas monotone. En effet, le test de Bingham, le test classique dans le cas axial, n'est pas optimal à ${\pmb \theta}_n$ inconnu et $p$ fixé, et ne détecte pas les contre-hypothèses contiguës en grande dimension. C'est pourquoi nous nous tournons vers des tests basés sur les plus grande et plus petite valeurs propres de la matrice de variance-covariance et nous déterminons leurs distributions asymptotiques sous les contre-hypothèses contiguës à $p$ fixé.Enfin, à l'aide d'un théorème central limite pour martingales, nous montrons que sous certaines conditions et après standardisation, les statistiques de Rayleigh et de Bingham sont asymptotiquement normales sous l'hypothèse d'invariance par rotation des observations. Ce résultat permet non seulement d'identifier le taux auquel le test de Bingham détecte des contre-hypothèses axiales mais aussi celui auquel il détecte des contre-hypothèses monotones.In this thesis we are interested in testing uniformity in high dimensions on the unit sphere $S^{p_n-1}$ (the dimension of the observations, $p_n$, depends on their number, and high-dimensional data are such that $p_n$ diverges to infinity with $n$).We consider first ``monotone'' alternatives whose density increases along an axis ${\pmb \theta}_n\in S^{p_n-1}$ and depends on a concentration parameter $\kappa_n>0$. We start by identifying the rate at which these alternatives are contiguous to uniformity; then we show thanks to local asymptotic normality results that the most classical test of uniformity, the Rayleigh test, is not optimal when ${\pmb \theta}_n$ is specified but becomes optimal when $p$ is fixed and in the high-dimensional FvML case when ${\pmb \theta}_n$ is unspecified.We consider next ``axial'' alternatives, assigning the same probability to antipodal points. They also depend on a location parameter ${\pmb \theta}_n\in S^{p_n-1}$ and a concentration parameter $\kappa_n\in\R$. The contiguity rate proves to be higher in that case and implies that the problem is more difficult than in the monotone case. Indeed, the Bingham test, the classical test when dealing with axial data, is not optimal when $p$ is fixed and ${\pmb \theta}_n$ is not specified, and is blind to the contiguous alternatives in high dimensions. This is why we turn to tests based on the extreme eigenvalues of the covariance matrix and establish their fixed-$p$ asymptotic distributions under contiguous alternatives.Finally, thanks to a martingale central limit theorem, we show that, under some assumptions and after standardisation, the Rayleigh and Bingham test statistics are asymptotically normal under general rotationally symmetric distributions. It enables us to identify the rate at which the Bingham test detects axial alternatives and also monotone alternatives.Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe

Tests of Concentration for Low-Dimensional and High-Dimensional Directional Data

We consider asymptotic inference for the concentration of directional data. More precisely, wepropose tests for concentration (i) in the low-dimensional case where the sample size n goes to infinity andthe dimension p remains fixed, and (ii) in the high-dimensional case where both n and p become arbitrarilylarge. To the best of our knowledge, the tests we provide are the first procedures for concentration thatare valid in the (n; p)-asymptotic framework. Throughout, we consider parametric FvML tests, that areguaranteed to meet asymptotically the nominal level constraint under FvML distributions only, as well as“pseudo-FvML” versions of such tests, that are validity-robust within the class of rotationally symmetricdistributions.We conduct a Monte-Carlo study to check our asymptotic results and to investigate the finitesamplebehavior of the proposed tests.info:eu-repo/semantics/publishe

Testing uniformity on high-dimensional spheres: the non-null behaviour of the Bingham test

info:eu-repo/semantics/publishe

Testing Uniformity on High-Dimensional Spheres against Contiguous Rotationally Symmetric Alternatives

info:eu-repo/semantics/publishe

On the power of axial tests of uniformity on spheres

Testing uniformity on the p-dimensional unit sphere is arguably the most fundamental problem in directional statistics. In this paper, we consider this problem in the framework of axial data, that is, under the assumption that the n observations at hand are randomly drawn from a distribution that charges antipodal regions equally. More precisely, we focus on axial, rotationally symmetric, alternatives and first address the problem under which the direction θ of the corresponding symmetry axis is specified. In this setup, we obtain Le Cam optimal tests of uniformity, that are based on the sample covariance matrix (unlike their non-axial analogs, that are based on the sample average). For the more important unspecified-θ problem, some classical tests are available in the literature, but virtually nothing is known on their non-null behavior. We therefore study the nonnull behavior of the celebrated Bingham test and of other tests that exploit the single-spiked nature of the considered alternatives. We perform Monte Carlo exercises to investigate the finite-sample behavior of our tests and to show their agreement with our asymptotic results.SCOPUS: ar.jinfo:eu-repo/semantics/publishe