7,374 research outputs found
On the interpretation of the WTP/WTA gap as imprecise utility: an axiomatic analysis
The willingness-to-pay (WTP) and willingness-to-accept (WTA) disparity reported in a rich empirical literature suggests that people have only an imprecise idea of how valuable a good is to them. In this note, we provide axioms that formally relate this imprecision in the evaluation of a good to the imprecision in the utility function, in the sense that x is strictly preferred to y iff the WTP for x is larger than the WTA for y. The preference relation is therefore an interval order (Fishburn (1970)) with ``interval utility' equal to the WTP/WTA interval itself. Applications to preference for liquidity and the strength of the status quo bias are given.WTA/WTP gap, interval orders, imprecise utility, reference-dependent preferences, status quo bias
Simple Computational Methods for Measuring the Difference of Empirical Distributions: Application to Internal and External Scope Tests in Contingent Valuation
This paper develops a statistically unbiased and simple method for measuring the difference of independent empirical distributions estimated by bootstrapping or other simulation approaches. This complete combinatorial method is compared with other unbiased and biased methods that have been suggested in the literature, first in Monte Carlo simulations and then in a field test of external and internal scope testing in contingent valuation. Tradeoffs between methods are discussed. When the empirical distributions are not independent a straightforward difference test is suggested.Research Methods/ Statistical Methods,
Random matrix ensembles associated with Lax matrices
A method to generate new classes of random matrix ensembles is proposed.
Random matrices from these ensembles are Lax matrices of classically integrable
systems with a certain distribution of momenta and coordinates. The existence
of an integrable structure permits to calculate the joint distribution of
eigenvalues for these matrices analytically. Spectral statistics of these
ensembles are quite unusual and in many cases give rigorously new examples of
intermediate statistics
Perturbation approach to multifractal dimensions for certain critical random matrix ensembles
Fractal dimensions of eigenfunctions for various critical random matrix
ensembles are investigated in perturbation series in the regimes of strong and
weak multifractality. In both regimes we obtain expressions similar to those of
the critical banded random matrix ensemble extensively discussed in the
literature. For certain ensembles, the leading-order term for weak
multifractality can be calculated within standard perturbation theory. For
other models such a direct approach requires modifications which are briefly
discussed. Our analytical formulas are in good agreement with numerical
calculations.Comment: 28 pages, 7 figure
A note on the error analysis of classical Gram-Schmidt
An error analysis result is given for classical Gram--Schmidt factorization
of a full rank matrix into where is left orthogonal (has
orthonormal columns) and is upper triangular. The work presented here shows
that the computed satisfies \normal{R}=\normal{A}+E where is an
appropriately small backward error, but only if the diagonals of are
computed in a manner similar to Cholesky factorization of the normal equations
matrix.
A similar result is stated in [Giraud at al, Numer. Math.
101(1):87--100,2005]. However, for that result to hold, the diagonals of
must be computed in the manner recommended in this work.Comment: 12 pages This v2. v1 (from 2006) has not the biliographical reference
set (at all). This is the only modification between v1 and v2. If you want to
quote this paper, please quote the version published in Numerische Mathemati
Coordinates, modes and maps for the density functional
Special bases of orthogonal polynomials are defined, that are suited to
expansions of density and potential perturbations under strict particle number
conservation. Particle-hole expansions of the density response to an arbitrary
perturbation by an external field can be inverted to generate a mapping between
density and potential. Information is obtained for derivatives of the
Hohenberg-Kohn functional in density space. A truncation of such an information
in subspaces spanned by a few modes is possible. Numerical examples illustrate
these algorithms.Comment: 15 pages, 9 figure
Entanglement of localized states
We derive exact expressions for the mean value of Meyer-Wallach entanglement
Q for localized random vectors drawn from various ensembles corresponding to
different physical situations. For vectors localized on a randomly chosen
subset of the basis, tends for large system sizes to a constant which
depends on the participation ratio, whereas for vectors localized on adjacent
basis states it goes to zero as a constant over the number of qubits.
Applications to many-body systems and Anderson localization are discussed.Comment: 6 pages, 4 figure
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