Detecting the direction of a signal on high-dimensional spheres: Non-null and Le Cam optimality results

We consider one of the most important problems in directional statistics, namely the problem of testing the null hypothesis that the spike direction $\theta$ of a Fisher-von Mises-Langevin distribution on the $p$-dimensional unit hypersphere is equal to a given direction $\theta_0$. After a reduction through invariance arguments, we derive local asymptotic normality (LAN) results in a general high-dimensional framework where the dimension $p_n$ goes to infinity at an arbitrary rate with the sample size $n$, and where the concentration $\kappa_n$ behaves in a completely free way with $n$, which offers a spectrum of problems ranging from arbitrarily easy to arbitrarily challenging ones. We identify various asymptotic regimes, depending on the convergence/divergence properties of $(\kappa_n)$, that yield different contiguity rates and different limiting experiments. In each regime, we derive Le Cam optimal tests under specified $\kappa_n$ and we compute, from the Le Cam third lemma, asymptotic powers of the classical Watson test under contiguous alternatives. We further establish LAN results with respect to both spike direction and concentration, which allows us to discuss optimality also under unspecified $\kappa_n$. To investigate the non-null behavior of the Watson test outside the parametric framework above, we derive its local asymptotic powers through martingale CLTs in the broader, semiparametric, model of rotationally symmetric distributions. A Monte Carlo study shows that the finite-sample behaviors of the various tests remarkably agree with our asymptotic results.Comment: 47 pages, 4 figure

Self-rated health among Mayan women participating in a randomised intervention trial reducing indoor air pollution in Guatemala

<p>Abstract</p> <p>Background</p> <p>Indoor air pollution (IAP) from solid fuels is a serious health problem in low-income countries that can be alleviated using improved stoves. Although women are the principal users, few studies have investigated the self-assessed impact of the stoves on their health and lives.</p> <p>Methods</p> <p>This study was conducted in rural highland Guatemala, involving 89 intervention and 80 control Mayan Indian young women (mean 27.8 years, SD 7.2). Outcomes were assessed after approximately 18 months use of the new stove. Our objectives were to compare self-rated health and change in health among women participating in a randomised control trial comparing a chimney stove with an open fire, to describe impacts on women's daily lives and their perceptions of how reduced kitchen smoke affects their own and their children's health.</p> <p>Results</p> <p>On intention-to-treat analysis, 52.8% of intervention women reported improvement in health, compared to 23.8% of control women (p < 0.001). Among 84 intervention women who reported reduced kitchen smoke as an important change, 88% linked this to improvement in their own health, particularly for non-respiratory symptoms (for example eye discomfort, headache); 57% linked reduced smoke to improvement in their children's health, particularly sore eyes.</p> <p>Conclusion</p> <p>Women's perception of their health was improved, but although smoke reduction was valued, this was linked mainly with alleviation of non-respiratory symptoms like eye discomfort and headache. More focus on such symptoms may help in promoting demand for improved stoves and cleaner fuels, but education about more severe consequences of IAP exposure is also required.</p

Sine-skewed circular distributions

Circular statistics, Finite mixtures, Jones–Pewsey family, Likelihood-based inference, Modality, Trigonometric moments, 60E05, 62H11,