5,200 research outputs found
Shaping Social Activity by Incentivizing Users
Events in an online social network can be categorized roughly into endogenous
events, where users just respond to the actions of their neighbors within the
network, or exogenous events, where users take actions due to drives external
to the network. How much external drive should be provided to each user, such
that the network activity can be steered towards a target state? In this paper,
we model social events using multivariate Hawkes processes, which can capture
both endogenous and exogenous event intensities, and derive a time dependent
linear relation between the intensity of exogenous events and the overall
network activity. Exploiting this connection, we develop a convex optimization
framework for determining the required level of external drive in order for the
network to reach a desired activity level. We experimented with event data
gathered from Twitter, and show that our method can steer the activity of the
network more accurately than alternatives
Maximin Safety: When Failing to Lose is Preferable to Trying to Win
We present a new decision rule, \emph{maximin safety}, that seeks to maintain
a large margin from the worst outcome, in much the same way minimax regret
seeks to minimize distance from the best. We argue that maximin safety is
valuable both descriptively and normatively. Descriptively, maximin safety
explains the well-known \emph{decoy effect}, in which the introduction of a
dominated option changes preferences among the other options. Normatively, we
provide an axiomatization that characterizes preferences induced by maximin
safety, and show that maximin safety shares much of the same behavioral basis
with minimax regret.Comment: 14 page
Multicriteria ranking using weights which minimize the score range
Various schemes have been proposed for generating a set of non-subjective weights when aggregating multiple criteria for the purposes of ranking or selecting alternatives. The maximin approach chooses the weights which maximise the lowest score (assuming there is an upper bound to scores). This is equivalent to finding the weights which minimize the maximum deviation, or range, between the worst and best scores (minimax). At first glance this seems to be an equitable way of apportioning weight, and the Rawlsian theory of justice has been cited in its support.We draw a distinction between using the maximin rule for the purpose of assessing performance, and using it for allocating resources amongst the alternatives. We demonstrate that it has a number of drawbacks which make it inappropriate for the assessment of performance. Specifically, it is tantamount to allowing the worst performers to decide the worth of the criteria so as to maximise their overall score. Furthermore, when making a selection from a list of alternatives, the final choice is highly sensitive to the removal or inclusion of alternatives whose performance is so poor that they are clearly irrelevant to the choice at hand
Testing the isotropy of high energy cosmic rays using spherical needlets
For many decades, ultrahigh energy charged particles of unknown origin that
can be observed from the ground have been a puzzle for particle physicists and
astrophysicists. As an attempt to discriminate among several possible
production scenarios, astrophysicists try to test the statistical isotropy of
the directions of arrival of these cosmic rays. At the highest energies, they
are supposed to point toward their sources with good accuracy. However, the
observations are so rare that testing the distribution of such samples of
directional data on the sphere is nontrivial. In this paper, we choose a
nonparametric framework that makes weak hypotheses on the alternative
distributions and allows in turn to detect various and possibly unexpected
forms of anisotropy. We explore two particular procedures. Both are derived
from fitting the empirical distribution with wavelet expansions of densities.
We use the wavelet frame introduced by [SIAM J. Math. Anal. 38 (2006b) 574-594
(electronic)], the so-called needlets. The expansions are truncated at scale
indices no larger than some , and the distances between
those estimates and the null density are computed. One family of tests (called
Multiple) is based on the idea of testing the distance from the null for each
choice of , whereas the so-called PlugIn approach is
based on the single full expansion, but with thresholded wavelet
coefficients. We describe the practical implementation of these two procedures
and compare them to other methods in the literature. As alternatives to
isotropy, we consider both very simple toy models and more realistic
nonisotropic models based on Physics-inspired simulations. The Monte Carlo
study shows good performance of the Multiple test, even at moderate sample
size, for a wide sample of alternative hypotheses and for different choices of
the parameter . On the 69 most energetic events published by the
Pierre Auger Collaboration, the needlet-based procedures suggest statistical
evidence for anisotropy. Using several values for the parameters of the
methods, our procedures yield -values below 1%, but with uncontrolled
multiplicity issues. The flexibility of this method and the possibility to
modify it to take into account a large variety of extensions of the problem
make it an interesting option for future investigation of the origin of
ultrahigh energy cosmic rays.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS619 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Note on Minimax Testing and Confidence Intervals in Moment Inequality Models
This note uses a simple example to show how moment inequality models used in
the empirical economics literature lead to general minimax relative efficiency
comparisons. The main point is that such models involve inference on a low
dimensional parameter, which leads naturally to a definition of "distance"
that, in full generality, would be arbitrary in minimax testing problems. This
definition of distance is justified by the fact that it leads to a duality
between minimaxity of confidence intervals and tests, which does not hold for
other definitions of distance. Thus, the use of moment inequalities for
inference in a low dimensional parametric model places additional structure on
the testing problem, which leads to stronger conclusions regarding minimax
relative efficiency than would otherwise be possible
Adaptive goodness-of-fit tests in a density model
Given an i.i.d. sample drawn from a density , we propose to test that
equals some prescribed density or that belongs to some
translation/scale family. We introduce a multiple testing procedure based on an
estimation of the -distance between and or between
and the parametric family that we consider. For each sample size , our test
has level of significance . In the case of simple hypotheses, we prove
that our test is adaptive: it achieves the optimal rates of testing established
by Ingster [J. Math. Sci. 99 (2000) 1110--1119] over various classes of smooth
functions simultaneously. As for composite hypotheses, we obtain similar
results up to a logarithmic factor. We carry out a simulation study to compare
our procedures with the Kolmogorov--Smirnov tests, or with goodness-of-fit
tests proposed by Bickel and Ritov [in Nonparametric Statistics and Related
Topics (1992) 51--57] and by Kallenberg and Ledwina [Ann. Statist. 23 (1995)
1594--1608].Comment: Published at http://dx.doi.org/10.1214/009053606000000119 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Adaptive Test of Conditional Moment Inequalities
In this paper, I construct a new test of conditional moment inequalities,
which is based on studentized kernel estimates of moment functions with many
different values of the bandwidth parameter. The test automatically adapts to
the unknown smoothness of moment functions and has uniformly correct asymptotic
size. The test has high power in a large class of models with conditional
moment inequalities. Some existing tests have nontrivial power against
n^{-1/2}-local alternatives in a certain class of these models whereas my
method only allows for nontrivial testing against (n/\log n)^{-1/2}-local
alternatives in this class. There exist, however, other classes of models with
conditional moment inequalities where the mentioned tests have much lower power
in comparison with the test developed in this paper
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