24,372 research outputs found
Smooth Solutions and Discrete Imaginary Mass of the Klein-Gordon Equation in the de Sitter Background
Using methods in the theory of semisimple Lie algebras, we can obtain all
smooth solutions of the Klein-Gordon equation on the 4-dimensional de Sitter
spacetime (dS^4). The mass of a Klein-Gordon scalar on dS^4 is related to an
eigenvalue of the Casimir operator of so(1,4). Thus it is discrete, or
quantized. Furthermore, the mass m of a Klein-Gordon scalar on dS^4 is
imaginary: m^2 being proportional to -N(N+3), with N >= 0 an integer.Comment: 23 pages, 4 figure
Statistical inference for semiparametric varying-coefficient partially linear models with error-prone linear covariates
We study semiparametric varying-coefficient partially linear models when some
linear covariates are not observed, but ancillary variables are available.
Semiparametric profile least-square based estimation procedures are developed
for parametric and nonparametric components after we calibrate the error-prone
covariates. Asymptotic properties of the proposed estimators are established.
We also propose the profile least-square based ratio test and Wald test to
identify significant parametric and nonparametric components. To improve
accuracy of the proposed tests for small or moderate sample sizes, a wild
bootstrap version is also proposed to calculate the critical values. Intensive
simulation experiments are conducted to illustrate the proposed approaches.Comment: Published in at http://dx.doi.org/10.1214/07-AOS561 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A Generic Path Algorithm for Regularized Statistical Estimation
Regularization is widely used in statistics and machine learning to prevent
overfitting and gear solution towards prior information. In general, a
regularized estimation problem minimizes the sum of a loss function and a
penalty term. The penalty term is usually weighted by a tuning parameter and
encourages certain constraints on the parameters to be estimated. Particular
choices of constraints lead to the popular lasso, fused-lasso, and other
generalized penalized regression methods. Although there has been a lot
of research in this area, developing efficient optimization methods for many
nonseparable penalties remains a challenge. In this article we propose an exact
path solver based on ordinary differential equations (EPSODE) that works for
any convex loss function and can deal with generalized penalties as well
as more complicated regularization such as inequality constraints encountered
in shape-restricted regressions and nonparametric density estimation. In the
path following process, the solution path hits, exits, and slides along the
various constraints and vividly illustrates the tradeoffs between goodness of
fit and model parsimony. In practice, the EPSODE can be coupled with AIC, BIC,
or cross-validation to select an optimal tuning parameter. Our
applications to generalized regularized generalized linear models,
shape-restricted regressions, Gaussian graphical models, and nonparametric
density estimation showcase the potential of the EPSODE algorithm.Comment: 28 pages, 5 figure
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