9,373 research outputs found
On the acceleration of some empirical means with application to nonparametric regression
Let be an i.i.d. sequence of random variables in ,
, for some function , under regularity conditions,
we show that \begin{align*} n^{1/2} \left(n^{-1} \sum_{i=1}^n
\frac{\varphi(X_i)}{\w f^{(i)}(X_i)}-\int_{} \varphi(x)dx \right)
\overset{\P}{\lr} 0, \end{align*} where \w f^{(i)} is the classical
leave-one-out kernel estimator of the density of . This result is striking
because it speeds up traditional rates, in root , derived from the central
limit theorem when \w f^{(i)}=f. As a consequence, it improves the classical
Monte Carlo procedure for integral approximation. The paper mainly addressed
with theoretical issues related to the later result (rates of convergence,
bandwidth choice, regularity of ) but also interests some statistical
applications dealing with random design regression. In particular, we provide
the asymptotic normality of the estimation of the linear functionals of a
regression function on which the only requirement is the H\"older regularity.
This leads us to a new version of the \textit{average derivative estimator}
introduced by H\"ardle and Stoker in \cite{hardle1989} which allows for
\textit{dimension reduction} by estimating the \textit{index space} of a
regression
Bootstrap Testing of the Rank of a Matrix via Least Squared Constrained Estimation
In order to test if an unknown matrix has a given rank (null hypothesis), we
consider the family of statistics that are minimum squared distances between an
estimator and the manifold of fixed-rank matrix. Under the null hypothesis,
every statistic of this family converges to a weighted chi-squared
distribution. In this paper, we introduce the constrained bootstrap to build
bootstrap estimate of the law under the null hypothesis of such statistics. As
a result, the constrained bootstrap is employed to estimate the quantile for
testing the rank. We provide the consistency of the procedure and the
simulations shed light one the accuracy of the constrained bootstrap with
respect to the traditional asymptotic comparison. More generally, the results
are extended to test if an unknown parameter belongs to a sub-manifold locally
smooth. Finally, the constrained bootstrap is easy to compute, it handles a
large family of tests and it works under mild assumptions
Integral approximation by kernel smoothing
Let be an i.i.d. sequence of random variables in
, . We show that, for any function , under regularity conditions, where
is the classical kernel estimator of the density of . This
result is striking because it speeds up traditional rates, in root , derived
from the central limit theorem when . Although this paper
highlights some applications, we mainly address theoretical issues related to
the later result. We derive upper bounds for the rate of convergence in
probability. These bounds depend on the regularity of the functions
and , the dimension and the bandwidth of the kernel estimator
. Moreover, they are shown to be accurate since they are used as
renormalizing sequences in two central limit theorems each reflecting different
degrees of smoothness of . As an application to regression modelling
with random design, we provide the asymptotic normality of the estimation of
the linear functionals of a regression function. As a consequence of the above
result, the asymptotic variance does not depend on the regression function.
Finally, we debate the choice of the bandwidth for integral approximation and
we highlight the good behavior of our procedure through simulations.Comment: Published at http://dx.doi.org/10.3150/15-BEJ725 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm). arXiv admin
note: text overlap with arXiv:1312.449
A generic framework for video understanding applied to group behavior recognition
This paper presents an approach to detect and track groups of people in
video-surveillance applications, and to automatically recognize their behavior.
This method keeps track of individuals moving together by maintaining a spacial
and temporal group coherence. First, people are individually detected and
tracked. Second, their trajectories are analyzed over a temporal window and
clustered using the Mean-Shift algorithm. A coherence value describes how well
a set of people can be described as a group. Furthermore, we propose a formal
event description language. The group events recognition approach is
successfully validated on 4 camera views from 3 datasets: an airport, a subway,
a shopping center corridor and an entrance hall.Comment: (20/03/2012
Integral estimation based on Markovian design
Suppose that a mobile sensor describes a Markovian trajectory in the ambient
space. At each time the sensor measures an attribute of interest, e.g., the
temperature. Using only the location history of the sensor and the associated
measurements, the aim is to estimate the average value of the attribute over
the space. In contrast to classical probabilistic integration methods, e.g.,
Monte Carlo, the proposed approach does not require any knowledge on the
distribution of the sensor trajectory. Probabilistic bounds on the convergence
rates of the estimator are established. These rates are better than the
traditional "root n"-rate, where n is the sample size, attached to other
probabilistic integration methods. For finite sample sizes, the good behaviour
of the procedure is demonstrated through simulations and an application to the
evaluation of the average temperature of oceans is considered.Comment: 45 page
Stubborn Learning
The paper studies a specific reinforcement learning rule in two-player games when each player faces a unidimensional strategy set. The essential feature of the rule is that a player keeps on incrementing her strategy in the same direction if and only if her utility increases. The paper concentrates on games on the square [0; 1] x [0; 1] with bilinear payoff functions such as the mixed extensions of 2 x 2 games. It studies the behavior of the system in the interior as well as on the borders of the strategy space. It precisely exhibits the trajectories of the system and the asymptotic states for symmetric, zero-sum, and twin games.
Enterprise model verification and validation : an approach
This article presents a verification and validation approach which is used here in order to complete the classical tool box the industrial user may utilize in enterprise modeling and integration domain. This approach, which has been defined independently from any application domain is based on several formal concepts and tools presented in this paper. These concepts are property concepts, property reference matrix, properties graphs, enterprise modeling domain ontology, conceptual graphs and formal reasoning mechanisms
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