Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract Non-parametric data envelopment analysis (DEA) estimators based on linear programming methods have been widely applied in analyses of productive efficiency. The distributions of these estimators remain unknown except in the simple case of one input and one output, and previous bootstrap methods proposed for inference have not been proven consistent, making inference doubtful. This paper derives the asymptotic distribution of DEA estimators under variable returns-to-scale. This result is then used to prove that two different bootstrap procedures (one based on sub-sampling, the other based on smoothing) provide consistent inference. The smooth bootstrap requires smoothing the irregularly-bounded density of inputs and outputs as well as smoothing of the DEA frontier estimate. Both bootstrap procedures allow for dependence of the inefficiency process on output levels and the mix of inputs in the case of input-oriented measures, or on inputs levels and the mix of outputs in the case of output-oriented measures.
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The paper considers functional linear regression, where scalar responses
$Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We
propose a smoothing splines estimator for the functional slope parameter based
on a slight modification of the usual penalty. Theoretical analysis
concentrates on the error in an out-of-sample prediction of the response for a
new random function $X_{n+1}$. It is shown that rates of convergence of the
prediction error depend on the smoothness of the slope function and on the
structure of the predictors. We then prove that these rates are optimal in the
sense that they are minimax over large classes of possible slope functions and
distributions of the predictive curves. For the case of models with
errors-in-variables the smoothing spline estimator is modified by using a
denoising correction of the covariance matrix of discretized curves. The
methodology is then applied to a real case study where the aim is to predict
the maximum of the concentration of ozone by using the curve of this
concentration measured the preceding day.Comment: Published in at http://dx.doi.org/10.1214/07-AOS563 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Efficiency scores of production units are measured
by their distance to an estimated production frontier.
Nonparametric data envelopment analysis estimators are
based on a finite sample of observed production units,
and radial distances are considered. We investigate the
consistency and the speed of convergence of these estimated
efficiency scores (or of the radial distances) in the very
general setup of a multi-output and multi-input case. It
is shown that the speed of convergence relies on the smoothness
of the unknown frontier and on the number of inputs and
outputs. Furthermore, one has to distinguish between the
output- and the input-oriented cases.
Functional principal component analysis (FPCA) based on the
Karhunen--Lo\`{e}ve decomposition has been successfully applied in many
applications, mainly for one sample problems. In this paper we consider common
functional principal components for two sample problems. Our research is
motivated not only by the theoretical challenge of this data situation, but
also by the actual question of dynamics of implied volatility (IV) functions.
For different maturities the log-returns of IVs are samples of (smooth) random
functions and the methods proposed here study the similarities of their
stochastic behavior. First we present a new method for estimation of functional
principal components from discrete noisy data. Next we present the two sample
inference for FPCA and develop the two sample theory. We propose bootstrap
tests for testing the equality of eigenvalues, eigenfunctions, and mean
functions of two functional samples, illustrate the test-properties by
simulation study and apply the method to the IV analysis.Comment: Published in at http://dx.doi.org/10.1214/07-AOS516 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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