10,656 research outputs found
Nonlinear State-Space Models for Microeconometric Panel Data
In applied microeconometric panel data analyses, time-constant random effects and first-order Markov chains are the most prevalent structures to account for intertemporal correlations in limited dependent variable models. An example from health economics shows that the addition of a simple autoregressive error terms leads to a more plausible and parsimonious model which also captures the dynamic features better. The computational problems encountered in the estimation of such models - and a broader class formulated in the framework of nonlinear state space models - hampers their widespread use. This paper discusses the application of different nonlinear filtering approaches developed in the time-series literature to these models and suggests that a straightforward algorithm based on sequential Gaussian quadrature can be expected to perform well in this setting. This conjecture is impressively confirmed by an extensive analysis of the example application
The physics of exceptional points
A short resume is given about the nature of exceptional points (EPs) followed
by discussions about their ubiquitous occurrence in a great variety of physical
problems. EPs feature in classical as well as in quantum mechanical problems.
They are associated with symmetry breaking for -symmetric
Hamiltonians, where a great number of experiments have been performed in
particular in optics, and to an increasing extent in atomic and molecular
physics. EPs are involved in quantum phase transition and quantum chaos, they
produce dramatic effects in multichannel scattering, specific time dependence
and more. In nuclear physics they are associated with instabilities and
continuum problems. Being spectral singularities they also affect approximation
schemes.Comment: 13 pages, 2 figure
Exceptional Points of Non-hermitian Operators
Exceptional points associated with non-hermitian operators, i.e. operators
being non-hermitian for real parameter values, are investigated. The specific
characteristics of the eigenfunctions at the exceptional point are worked out.
Within the domain of real parameters the exceptional points are the points
where eigenvalues switch from real to complex values. These and other results
are exemplified by a classical problem leading to exceptional points of a
non-hermitian matrix.Comment: 8 pages, Latex, four figures, submitted to EPJ
Phases of Wave Functions and Level Repulsion
Avoided level crossings are associated with exceptional points which are the
singularities of the spectrum and eigenfunctions, when they are considered as
functions of a coupling parameter. It is shown that the wave function of {\it
one} state changes sign but not the other, if the exceptional point is
encircled in the complex plane. An experimental setup is suggested where this
peculiar phase change could be observed.Comment: 4 pages Latex, 2 figures encapsulated postscripts (*.epsi) submitted
to The European Physical Journal
Nonlinear State-Space Models for Microeconometric Panel Data
In applied microeconometric panel data analyses, time-constant random effects and first-order Markov chains are the most prevalent structures to account for intertemporal correlations in limited dependent variable models. An example from health economics shows that the addition of a simple autoregressive error terms leads to a more plausible and parsimonious model which also captures the dynamic features better. The computational problems encountered in the estimation of such models - and a broader class formulated in the framework of nonlinear state space models - hampers their widespread use. This paper discusses the application of different nonlinear filtering approaches developed in the time-series literature to these models and suggests that a straightforward algorithm based on sequential Gaussian quadrature can be expected to perform well in this setting. This conjecture is impressively confirmed by an extensive analysis of the example application.LDV models; panel data; state space; numerical integration; health
Specification(s) of Nested Logit Models
The nested logit model has become an important tool for the empirical analysis of discrete outcomes. There is some confusion about its specification of the outcome probabilities. Two major variants show up in the literature. This paper compares both and finds that one of them (called random utility maximization nested logit, RUMNL) is preferable in most situations. Since the command nlogit of Stata 7.0 implements the other variant (called non-normalized nested logit, NNNL), an implementation of RUMNL called nlogitrum is introduced. Numerous examples support and illustrate the differences of both specifications.
Estimation with Numerical Integration on Sparse Grids
For the estimation of many econometric models, integrals without analytical solutions have to be evaluated. Examples include limited dependent variables and nonlinear panel data models. In the case of one-dimensional integrals, Gaussian quadrature is known to work efficiently for a large class of problems. In higher dimensions, similar approaches discussed in the literature are either very specific and hard to implement or suffer from exponentially rising computational costs in the number of dimensions - a problem known as the "curse of dimensionality" of numerical integration. We propose a strategy that shares the advantages of Gaussian quadrature methods, is very general and easily implemented, and does not suffer from the curse of dimensionality. Monte Carlo experiments for the random parameters logit model indicate the superior performance of the proposed method over simulation techniques
Quantum Chaos, Degeneracies and Exceptional Points
It is argued that, if a regular Hamiltonian is perturbed by a term that
produces chaos, the onset of chaos is shifted towards larger values of the
perturbation parameter if the unperturbed spectrum is degenerate and the
lifting of the degeneracy is of second order in this parameter. The argument is
based on the behaviour of the exceptional points of the full problem.Comment: RevTeX with 4 figs. available from the authors; to appear in
Phys.Rev.
Fano-Feshbach resonances in two-channel scattering around exceptional points
It is well known that in open quantum systems resonances can coalesce at an
exceptional point, where both the energies {\em and} the wave functions
coincide. In contrast to the usual behaviour of the scattering amplitude at one
resonance, the coalescence of two resonances invokes a pole of second order in
the Green's function, in addition to the usual first order pole. We show that
the interference due to the two pole terms of different order gives rise to
patterns in the scattering cross section which closely resemble Fano-Feshbach
resonances. We demonstrate this by extending previous work on the analogy of
Fano-Feshbach resonances to classical resonances in a system of two driven
coupled damped harmonic oscillators.Comment: 8 pages, 5 figures, submitted to J. Phys.
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