Saddlepoint approximations for likelihood ratio like statistics with applications to permutation tests

We obtain two theorems extending the use of a saddlepoint approximation to multiparameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be used in bootstrap approximations. In the first, we show that in some cases when no density exists, the integral of the formal saddlepoint density over the set corresponding to large values of the likelihood ratio-like statistic approximates the true probability with relative error of order $1/n$. In the second, we give multivariate generalizations of the Lugannani--Rice and Barndorff-Nielsen or $r^*$ formulas for the approximations. These theorems are applied to obtain permutation tests based on the likelihood ratio-like statistics for the $k$ sample and the multivariate two-sample cases. Numerical examples are given to illustrate the high degree of accuracy, and these statistics are compared to the classical statistics in both cases.Comment: Published in at http://dx.doi.org/10.1214/11-AOS945 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Do marital prospects dissuade unmarried fertility?

Unmarried fertility was a lot lower in the 1970s than in the 1990s. It was also the case that unmarried mothers had much lower marriage rates than non-mothers, a differential that has largely vanished over time. Could this marriage-market penalty have been strong enough to explain why unmarried fertility rates were lower then? To explore this issue, we introduce a new model of fertility and marriage, based on directed search. Relative to the existing literature, the essential contributions of the model are to allow for accumulation of children over the lifecycle and for the marriage of single mothers. We use the model, in conjunction with US survey data, to explore the impact of marital prospects on the fertility decisions of unmarried women. We find that the decline, from the 1970s to 1995, in marriage rates of unmarried women with no children, can account for the dramatic rise in unmarried women’s share of births over that period

The Algebra of Grand Unified Theories

The Standard Model of particle physics may seem complicated and arbitrary, but it has hidden patterns that are revealed by the relationship between three "grand unified theories": theories that unify forces and particles by extending the Standard Model symmetry group U(1) x SU(2) x SU(3) to a larger group. These three theories are Georgi and Glashow's SU(5) theory, Georgi's theory based on the group Spin(10), and the Pati-Salam model based on the group SU(2) x SU(2) x SU(4). In this expository account for mathematicians, we explain only the portion of these theories that involves finite-dimensional group representations. This allows us to reduce the prerequisites to a bare minimum while still giving a taste of the profound puzzles that physicists are struggling to solve.Comment: 73 pages, 20 ps figure

Fat Cats and Thin Kittens: Are People Who Make Large Campaign Contributions Different?

Critics of campaign finance in the United States often direct their fire toward contributors who make large donations. Critics charge that large contributions are unfair, unrepresentative, and undemocratic. Accordingly, they push for "reforms" that would favor small contributions over large, and public money over private donations. Survey data on contributors contradict that stereotype of contributors of large amounts and their effects on American politics. Overall, "fat cats" differ less from contributors of smaller amounts than critics have alleged. The differences that do exist are mostly unsurprising and generally small in magnitude. Survey results show that both policy liberalism and Democratic partisanship are well represented among contributors of large sums.The supporters of McCain-Feingold argue that new restrictions on large contributions will profoundly alter American politics for the better. Their claims have no basis in fact. New laws aimed at restricting large donations in favor of smaller ones will have little effect on practical politics

Scrutinising the British Monarchy: The corporate brand that was shaken, stirred and survived

Purpose – The principal purposes of this article are to provide normative advice in terms of managing the British Monarchy as a Corporate Heritage Brand and to reveal the efficacy of examining a brand’s history for corporate heritage brands generally. Design/methodology/approach – Taking a case history approach, this article examines critical events in the Crown’s history. This article is also informed by the diverse literatures on the British Monarchy and also marshals the identity literatures and the nascent literature relating to corporate brands. Six critical incidents that have shaped the monarchy over the last millennium provide the principal data source for this article. Findings - In scrutinising key events from the institution’s historiography it was found that the management and maintenance of the Crown as a corporate brand entail concern with issues relating to (1) continuity (maintaining heritage and symbolism), (2) visibility (having a meaningful and prominent public profile), (3) strategy (anticipating and enacting change), (4) sensitivity (rapid response to crises), (5) respectability (retaining public favour), and (6) empathy (acknowledging that brand ownership resides with the public). Taking an integrationist perspective, the efficacy of adopting a corporate marketing approach/philosophy is also highlighted. Research limitations – The insights derived from this article are based on the extant literatures on the Monarchy: richer insights would, of course, be derived from undertaking research within the institution. However, the difficulty in gaining access to the Royal Household in undertaking empirical/publishable research renders most methodologies currently used within management research virtually unavailable. Practical implications – There are two. In terms of the Crown a new tripartite dictum is offered which is broader in scope than Bagehot’s and takes account of the Monarchy’s constitutional, societal and symbolic obligations. As such, the Crown should be Dutiful to the tenets of a constitutional monarchy; Devoted to the peoples of the realm and Dedicated to maintaining royal symbolism. In terms of the management of corporate brands/heritage brands a five- faceted approach/modus operandi is introduced which is called: ‚Chronicling the Corporate Brand.‛ These are: (a) chronicling the brand’s history; (b) assembling a cross-section of individuals to set down the corporate brand narrative; (c) documenting and communicating the insights from the aforementioned (d) marshalling the narrative vis a vis corporate brand management/crisis management; (e) revisiting the brand’s history for new insights. Originality/value – This is one of the first articles to examine the British Monarchy through a corporate branding lens. It confirms that the Crown is analogous to a corporate brand and, therefore, ought to be managed as such

The Potential of Spaced-based High-Energy Neutrino Measurements via the Airshower Cherenkov Signal

Future space-based experiments, such as OWL and JEM-EUSO, view large atmospheric and terrestrial neutrino targets. With energy thresholds slightly above 10^19 eV for observing airshowers via air fluorescence, the potential for observing the cosmogenic neutrino flux associated with the GZK effect is limited. However, the forward Cherenkov signal associated with the airshower can be observed at much lower energies. A simulation was developed to determine the Cherenkov signal strength and spatial extent at low-Earth orbit for upward-moving airshowers. A model of tau neutrino interactions in the Earth was employed to determine the event rate of interactions that yielded a tau lepton which would induce an upward-moving airshower observable by a space-based instrument. The effect of neutrino attenuation by the Earth forces the viewing of the Earth's limb to observe the nu_tau-induced Cherenkov airshower signal at above the OWL Cherenkov energy threshold of ~10^16.5 eV for limb-viewed events. Furthermore, the neutrino attenuation limits the effective terrestrial neutrino target area to ~3x10^5 km^2 at 10^17 eV, for an orbit of 1000 km and an instrumental full Field-of-View of 45 degrees. This translates into an observable cosmogenic neutrino event rate of ~1/year based upon two different models of the cosmogenic neutrino flux, assuming neutrino oscillations and a 10% duty cycle for observation.Comment: Contribution to the 32nd ICRC, Beijing, China, August 2011; Paper#1331, 4 pages, 4 figure