2,702 research outputs found
Nonparametric IV estimation of shape-invariant Engel curves
This paper concerns the identification and estimation of a shape-invariant Engel
curve system with endogenous total expenditure. The shape-invariant specification
involves a common shift parameter for each demographic group in a pooled
system of Engel curves. Our focus is on the identification and estimation of both
the nonparametric shape of the Engel curve and the parametric specification of the
demographic scaling parameters. We present a new identification condition, closely
related to the concept of bounded completeness in statistics. 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 IV regression when the endogenous regressor has unbounded
support. Root-n asymptotic normality and semiparametric efficiency of
the parametric components are also given under a set of ‘low-level’ sufficient conditions.
Monte Carlo simulations shed lights on the choice of smoothing parameters
and demonstrate that the sieve IV estimator performs well. An application is made
to the estimation of Engel curves using the UK Family Expenditure Survey and
shows the importance of adjusting for endogeneity in terms of both the curvature
and demographic parameters of systems of Engel curves
Nonparametric IV estimation of shape-invariant Engel curves
This paper concerns the identification and estimation of a shape-invariant Engel curve system with endogenous total expenditure. The shape-invariant specification involves a common shift parameter for each demographic group in a pooled system of Engel curves. Our focus is on the identification and estimation of both the nonparametric shape of the Engel curve and the parametric specification of the demographic scaling parameters. We present a new identification condition, closely related to the concept of bounded completeness in statistics. 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 IV regression when the endogenous regressor has unbounded support. Root-n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of Ѭow-level' sufficient conditions. Monte Carlo simulations shed lights on the choice of smoothing parameters and demonstrate that the sieve IV estimator performs well. An application is made to the estimation of Engel curves using the UK Family Expenditure Survey and shows the importance of adjusting for endogeneity in terms of both the curvature and demographic parameters of systems of Engel curves.
Double coset construction of moduli space of holomorphic bundles and Hitchin systems
We present a description of the moduli space of holomorphic vector bundles
over Riemann curves as a double coset space which is differ from the standard
loop group construction. Our approach is based on equivalent definitions of
holomorphic bundles, based on the transition maps or on the first order
differential operators. Using this approach we present two independent
derivations of the Hitchin integrable systems. We define a "superfree" upstairs
systems from which Hitchin systems are obtained by three step hamiltonian
reductions. A special attention is being given on the Schottky parameterization
of curves.Comment: 19 pages, Late
Phonon renormalization from local and transitive electron-lattice couplings in strongly correlated systems
Within the time-dependent Gutzwiller approximation (TDGA) applied to
Holstein- and SSH-Hubbard models we study the influence of electron
correlations on the phonon self-energy. For the local Holstein coupling we find
that the phonon frequency renormalization gets weakened upon increasing the
onsite interaction for all momenta. In contrast, correlations can enhance
the phonon frequency shift for small wave-vectors in the SSH-Hubbard model.
Moreover the TDGA applied to the latter model provides a mechanism which leads
to phonon frequency corrections at intermediate momenta due to the coupling
with double occupancy fluctuations. Both models display a shift of the
nesting-induced to a instability when the onsite interaction becomes
sufficiently strong and thus establishing phase separation as a generic
phenomenon of strongly correlated electron-phonon coupled systems.Comment: 14 pages, 11 figure
Localization of the Riemann-Roch character
We present a K-theoritic approach to the Guillemin-Sternberg conjecture,
about the commutativity of geometric quantization and symplectic reduction,
which was proved by Meinrenken and Tian-Zhang. Besides providing a new proof of
this conjecture for the full non-abelian group action case, our methods lead to
a generalisation for compact Lie group actions on manifolds that are not
symplectic. Instead, these manifolds carry an invariant almost complex
structure and an abstract moment map.Comment: revised version, 55 page
The Lie group of real analytic diffeomorphisms is not real analytic
We construct an infinite dimensional real analytic manifold structure for the
space of real analytic mappings from a compact manifold to a locally convex
manifold. Here a map is real analytic if it extends to a holomorphic map on
some neighbourhood of the complexification of its domain. As is well known the
construction turns the group of real analytic diffeomorphisms into a smooth
locally convex Lie group. We prove then that the diffeomorphism group is
regular in the sense of Milnor.
In the inequivalent "convenient setting of calculus" the real analytic
diffeomorphisms even form a real analytic Lie group. However, we prove that the
Lie group structure on the group of real analytic diffeomorphisms is in general
not real analytic in our sense.Comment: 33 pages, LaTex, v2: now includes a proof for the regularity of the
real analytic diffeomorphism grou
Three Applications of Instanton Numbers
We use instanton numbers to: (i) stratify moduli of vector bundles, (ii)
calculate relative homology of moduli spaces and (iii) distinguish curve
singularities.Comment: To appear in Communications in Mathematical Physic
Covariant Symanzik identities
Classical isomorphism theorems due to Dynkin, Eisenbaum, Le Jan, and Sznitman
establish equalities between the correlation functions or distributions of
occupation times of random paths or ensembles of paths and Markovian fields,
such as the discrete Gaussian free field. We extend these results to the case
of real, complex, or quaternionic vector bundles of arbitrary rank over graphs
endowed with a connection, by providing distributional identities between
functionals of the Gaussian free vector field and holonomies of random paths.
As an application, we give a formula for computing moments of a large class of
random, in general non-Gaussian, fields in terms of holonomies of random paths
with respect to an annealed random gauge field, in the spirit of Symanzik's
foundational work on the subject.Comment: 51 pages, 10 figures. This version contains a new introduction, an
additional Section (6.8) detailing an important example (the case of
trace-positive holonomies), and a treatment of the quaternionic case. The
introductory material on continuous time random walks on multigraphs in
Section 1 was also simplifie
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