Berry-Esseen bounds for nonlinear statistics, and asymptotic relative efficiency between correlation statistics

Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall correlation statistics; conditions sufficient to ensure that the Spearman and Kendall statistics are equally (asymptotically) efficient are provided, and several models are considered which illustrate the use of such conditions. Lastly, the fourth paper proves that, in the bivariate normal model, the ARE between any of these correlation statistics possesses certain monotonicity properties; quadratic lower and upper bounds on the ARE are stated as direct applications of such monotonicity patterns.

COMPARISON OF NON-HEATING PALEOINTENSITY TECHNIQUES USING BASALTS FROM LEMPTÉGY VOLCANO, FRANCE AND SYNTHETIC MAGNETITE-BEARING SAMPLES

Data of the strength of Earth’s magnetic field (paleointensity) in the geological past are crucial for understanding the geodynamo. Conventional paleointensity determination methods require heating a sample to a high temperature in one or more steps. Consequently, many rocks are unsuitable for these methods due to a heating-induced experimental alteration. Alternative non-heating paleointensity methods are investigated to assess their effectiveness and reliability using both natural samples from Lemptégy Volcano, France, and synthetic samples. Paleointensity was measured from the natural and synthetic samples using the Pseudo-Thellier, ARM, REM, REMc, REM’, and Preisach methods. For the natural samples, only the Pseudo-Thellier method was able to produce a reasonable paleointensity estimate consistent with previous paleointensity data. The synthetic samples yielded more successful estimates using all the methods, with the Pseudo-Thellier and ARM methods producing the most accurate results. The Pseudo-Thellier method appears to be the best alternative to the heating-based paleointensity methods.