15,230 research outputs found
A Nonparametric Model of Frontiers
In this paper we propose a nonparametric regression frontier model that assumes no specific parametric family of densities for the unobserved stochastic component that represents efficiency in the model. Nonparametric estimation of the regression frontier is obtained using a local linear estimator that is shown to be consistent and asymptotically normal under standard assumptions. The estimator we propose envelops the data but is not inherently biased as Free Disposal Hull - FDH or Data Envelopment Analysis - DEA estimators. It is also more robust to extreme values than the aforementioned estimators. A Monte Carlo study is performed to provide preliminary evidence on the estimator's finite sample properties and to compare its performance to a bias corrected FDH estimatononparametric regression frontier, local linear estimation, U statistics.
Iteration of quadratic maps on matrix algebras
We study the iteration of a quadratic family in the algebra of 2 × 2 real matrices, parameterized by a matrix C. We analyze and classify the existing cycles (periodic orbits) and their dependence on the parameter matrix. We discuss how new dynamical phenomena occur as a consequence of the noncommutativity of the matrix product. In particular, we show that the commutator of the initial condition with parameter matrix C has a decisive role in the overall dynamics
Orbit Representations from Linear mod 1 Transformations
We show that every point carries a representation of a
-algebra that encodes the orbit structure of the linear mod 1 interval map
. Such -algebra is generated by
partial isometries arising from the subintervals of monotonicity of the
underlying map . Then we prove that such representation is
irreducible. Moreover two such of representations are unitarily equivalent if
and only if the points belong to the same generalized orbit, for every
and
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