3,004 research outputs found
A new kernel-based approach to system identification with quantized output data
In this paper we introduce a novel method for linear system identification
with quantized output data. We model the impulse response as a zero-mean
Gaussian process whose covariance (kernel) is given by the recently proposed
stable spline kernel, which encodes information on regularity and exponential
stability. This serves as a starting point to cast our system identification
problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods
to provide an estimate of the system. In particular, we design two methods
based on the so-called Gibbs sampler that allow also to estimate the kernel
hyperparameters by marginal likelihood maximization via the
expectation-maximization method. Numerical simulations show the effectiveness
of the proposed scheme, as compared to the state-of-the-art kernel-based
methods when these are employed in system identification with quantized data.Comment: 10 pages, 4 figure
Nonparametric frontier estimation from noisy data
A new nonparametric estimator of production frontiers is defined and studied when the data set of production units is contaminated by measurement error. The measurement error is assumed to be an additive normal random variable on the input variable, but its variance is unknown. The estimator is a modification of the m-frontier, which necessitates the computation of a consistent estimator of the conditional survival function of the input variable given the output variable. In this paper, the identification and the consistency of a new estimator of the survival function is proved in the presence of additive noise with unknown variance. The performance of the estimator is also studied through simulated data.production frontier, deconvolution, measurement error, efficiency analysis
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
Derivative-free online learning of inverse dynamics models
This paper discusses online algorithms for inverse dynamics modelling in
robotics. Several model classes including rigid body dynamics (RBD) models,
data-driven models and semiparametric models (which are a combination of the
previous two classes) are placed in a common framework. While model classes
used in the literature typically exploit joint velocities and accelerations,
which need to be approximated resorting to numerical differentiation schemes,
in this paper a new `derivative-free' framework is proposed that does not
require this preprocessing step. An extensive experimental study with real data
from the right arm of the iCub robot is presented, comparing different model
classes and estimation procedures, showing that the proposed `derivative-free'
methods outperform existing methodologies.Comment: 14 pages, 11 figure
Semi-nonparametric IV estimation of shape-invariant Engel curves
This paper studies a shape-invariant Engel curve system with endogenous total expenditure, in which the shape-invariant specification involves a common shift parameter for each demographic group in a pooled system of nonparametric Engel curves. We focus on the identification and estimation of both the nonparametric shapes of the Engel curves and the parametric specification of the demographic scaling parameters. The identification condition relates to the bounded completeness and the estimation procedure applies the sieve minimum distance estimation of conditional moment restrictions, allowing for endogeneity. We establish a new root mean squared convergence rate for the nonparametric instrumental variable regression when the endogenous regressor could have unbounded support. Root-n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of "low-level" sufficient conditions. Our empirical application using the U.K. Family Expenditure Survey shows the importance of adjusting for endogeneity in terms of both the nonparametric curvatures and the demographic parameters of systems of Engel curves
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