202,964 research outputs found
Stochastic Restricted Biased Estimators in misspecified regression model with incomplete prior information
In this article, the analysis of misspecification was extended to the
recently introduced stochastic restricted biased estimators when
multicollinearity exists among the explanatory variables. The Stochastic
Restricted Ridge Estimator (SRRE), Stochastic Restricted Almost Unbiased Ridge
Estimator (SRAURE), Stochastic Restricted Liu Estimator (SRLE), Stochastic
Restricted Almost Unbiased Liu Estimator (SRAULE), Stochastic Restricted
Principal Component Regression Estimator (SRPCR), Stochastic Restricted r-k
class estimator (SRrk) and Stochastic Restricted r-d class estimator (SRrd)
were examined in the misspecified regression model due to missing relevant
explanatory variables when incomplete prior information of the regression
coefficients is available. Further, the superiority conditions between
estimators and their respective predictors were obtained in the mean square
error matrix (MSEM) sense. Finally, a numerical example and a Monte Carlo
simulation study were used to illustrate the theoretical findings.Comment: 35 Pages, 6 Figure
Equilibrium Points of an AND-OR Tree: under Constraints on Probability
We study a probability distribution d on the truth assignments to a uniform
binary AND-OR tree. Liu and Tanaka [2007, Inform. Process. Lett.] showed the
following: If d achieves the equilibrium among independent distributions (ID)
then d is an independent identical distribution (IID). We show a stronger form
of the above result. Given a real number r such that 0 < r < 1, we consider a
constraint that the probability of the root node having the value 0 is r. Our
main result is the following: When we restrict ourselves to IDs satisfying this
constraint, the above result of Liu and Tanaka still holds. The proof employs
clever tricks of induction. In particular, we show two fundamental
relationships between expected cost and probability in an IID on an OR-AND
tree: (1) The ratio of the cost to the probability (of the root having the
value 0) is a decreasing function of the probability x of the leaf. (2) The
ratio of derivative of the cost to the derivative of the probability is a
decreasing function of x, too.Comment: 13 pages, 3 figure
On alpha stable distribution of wind driven water surface wave slope
We propose a new formulation of the probability distribution function of wind
driven water surface slope with an -stable distribution probability.
The mathematical formulation of the probability distribution function is given
under an integral formulation. Application to represent the probability of time
slope data from laboratory experiments is carried out with satisfactory
results. We compare also the -stable model of the water surface slopes
with the Gram-Charlier development and the non-Gaussian model of Liu et
al\cite{Liu}. Discussions and conclusions are conducted on the basis of the
data fit results and the model analysis comparison.Comment: final version of the manuscript: 25 page
Expansion of a compressible gas in vacuum
Tai-Ping Liu \cite{Liu\_JJ} introduced the notion of "physical solution' of
the isentropic Euler system when the gas is surrounded by vacuum. This notion
can be interpreted by saying that the front is driven by a force resulting from
a H\"older singularity of the sound speed. We address the question of when this
acceleration appears or when the front just move at constant velocity. We know
from \cite{Gra,SerAIF} that smooth isentropic flows with a non-accelerated
front exist globally in time, for suitable initial data. In even space
dimension, these solutions may persist for all ; we say that they are
{\em eternal}. We derive a sufficient condition in terms of the initial data,
under which the boundary singularity must appear. As a consequence, we show
that, in contrast to the even-dimensional case, eternal flows with a
non-accelerated front don't exist in odd space dimension. In one space
dimension, we give a refined definition of physical solutions. We show that for
a shock-free flow, their asymptotics as both ends are
intimately related to each other
A disk in the Galactic Center in the past ?
We raise the question whether in the past a disk could have existed in our
Galactic Center which has disappeared now. Our model for the interaction of a
cool disk and a hot corona above (Liu et al. 2004) allows to estimate an upper
limit for the mass that might have been present in a putative accretion disk
after a last star forming event, but would now have evaporated by coronal
action.Comment: 2 pages, Contribution to Conference Proc. "Growing Black Holes",
Garching, 2004, Eds. A. Merloni, S. Nayakshin, R. Sunyaev, Springer series
"ESO Astrophysics Symposia", in prin
Skew -Derivations on Semiprime Rings
For a ring with an automorphism , an -additive mapping
is called a skew
-derivation with respect to if it is always a -derivation
of for each argument. Namely, it is always a -derivation of for
the argument being left once arguments are fixed by elements in
. In this short note, starting from Bre\v{s}ar Theorems, we prove that a
skew -derivation () on a semiprime ring must map into the
center of .Comment: 8 page
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