13,430 research outputs found
Large-sample study of the kernel density estimators under multiplicative censoring
The multiplicative censoring model introduced in Vardi [Biometrika 76 (1989)
751--761] is an incomplete data problem whereby two independent samples from
the lifetime distribution , and
, are observed subject to a form of coarsening.
Specifically, sample is fully observed while
is observed instead of , where
and is an independent sample from the standard
uniform distribution. Vardi [Biometrika 76 (1989) 751--761] showed that this
model unifies several important statistical problems, such as the deconvolution
of an exponential random variable, estimation under a decreasing density
constraint and an estimation problem in renewal processes. In this paper, we
establish the large-sample properties of kernel density estimators under the
multiplicative censoring model. We first construct a strong approximation for
the process , where is a solution of the
nonparametric score equation based on , and
is the total sample size. Using this strong approximation and a result
on the global modulus of continuity, we establish conditions for the strong
uniform consistency of kernel density estimators. We also make use of this
strong approximation to study the weak convergence and integrated squared error
properties of these estimators. We conclude by extending our results to the
setting of length-biased sampling.Comment: Published in at http://dx.doi.org/10.1214/11-AOS954 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Proprioceptive Robot Collision Detection through Gaussian Process Regression
This paper proposes a proprioceptive collision detection algorithm based on
Gaussian Regression. Compared to sensor-based collision detection and other
proprioceptive algorithms, the proposed approach has minimal sensing
requirements, since only the currents and the joint configurations are needed.
The algorithm extends the standard Gaussian Process models adopted in learning
the robot inverse dynamics, using a more rich set of input locations and an
ad-hoc kernel structure to model the complex and non-linear behaviors due to
frictions in quasi-static configurations. Tests performed on a Universal Robots
UR10 show the effectiveness of the proposed algorithm to detect when a
collision has occurred.Comment: Published at ACC 201
Optimal Rate of Direct Estimators in Systems of Ordinary Differential Equations Linear in Functions of the Parameters
Many processes in biology, chemistry, physics, medicine, and engineering are
modeled by a system of differential equations. Such a system is usually
characterized via unknown parameters and estimating their 'true' value is thus
required. In this paper we focus on the quite common systems for which the
derivatives of the states may be written as sums of products of a function of
the states and a function of the parameters.
For such a system linear in functions of the unknown parameters we present a
necessary and sufficient condition for identifiability of the parameters. We
develop an estimation approach that bypasses the heavy computational burden of
numerical integration and avoids the estimation of system states derivatives,
drawbacks from which many classic estimation methods suffer. We also suggest an
experimental design for which smoothing can be circumvented. The optimal rate
of the proposed estimators, i.e., their -consistency, is proved and
simulation results illustrate their excellent finite sample performance and
compare it to other estimation approaches
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