21,459 research outputs found
The Minimal GUT with Inflaton and Dark Matter Unification
Giving up the solutions to the fine-tuning problems, we propose the
non-supersymmetric flipped model based on the minimal
particle content principle, which can be constructed from the four-dimensional
models, five-dimensional orbifold models, and local F-theory
models. To achieve gauge coupling unification, we introduce one pair
of vector-like fermions, which form complete
representation. Proton lifetime is around years, neutrino
masses and mixing can be explained via seesaw mechanism, baryon asymmetry can
be generated via leptogenesis, and vacuum stability problem can be solved as
well. In particular, we propose that inflaton and dark matter particle can be
unified to a real scalar field with symmetry, which is not an axion and
does not have the non-minimal coupling to gravity. Such kind of scenarios can
be applied to the generic scalar dark matter models. Also, we find that the
vector-like particle corrections to the masses can be about 6.6%, while
their corrections to the and masses are negligible.Comment: 5 pages, 4 figures;V2: published versio
Analysis of variance, coefficient of determination and -test for local polynomial regression
This paper provides ANOVA inference for nonparametric local polynomial
regression (LPR) in analogy with ANOVA tools for the classical linear
regression model. A surprisingly simple and exact local ANOVA decomposition is
established, and a local R-squared quantity is defined to measure the
proportion of local variation explained by fitting LPR. A global ANOVA
decomposition is obtained by integrating local counterparts, and a global
R-squared and a symmetric projection matrix are defined. We show that the
proposed projection matrix is asymptotically idempotent and asymptotically
orthogonal to its complement, naturally leading to an -test for testing for
no effect. A by-product result is that the asymptotic bias of the ``projected''
response based on local linear regression is of quartic order of the bandwidth.
Numerical results illustrate the behaviors of the proposed R-squared and
-test. The ANOVA methodology is also extended to varying coefficient models.Comment: Published in at http://dx.doi.org/10.1214/07-AOS531 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
- …