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Linear Case (linear + case)

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Mathematics and Statistics	50%

Selected Abstracts

Passive Hedge Fund Replication , Beyond the Linear Case

EUROPEAN FINANCIAL MANAGEMENT, Issue 2 2010
Noël Amenc
G10 Abstract In this paper we extend,Hasanhodzic and Lo (2007),by assessing the out-of-sample performance of various non-linear and conditional hedge fund replication models. We find that going beyond the linear case does not necessarily enhance the replication power. On the other hand, we find that selecting factors on the basis on an economic analysis allows for a substantial improvement in out-of-sample replication quality, whatever the underlying form of the factor model. Overall, we confirm the findings in,Hasanhodzic and Lo (2007)that the performance of the replicating strategies is systematically inferior to that of the actual hedge funds. [source]

LEVERAGE ADJUSTMENTS FOR DISPERSION MODELLING IN GENERALIZED NONLINEAR MODELS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 4 2009
Gordon K. Smyth
Summary For normal linear models, it is generally accepted that residual maximum likelihood estimation is appropriate when covariance components require estimation. This paper considers generalized linear models in which both the mean and the dispersion are allowed to depend on unknown parameters and on covariates. For these models there is no closed form equivalent to residual maximum likelihood except in very special cases. Using a modified profile likelihood for the dispersion parameters, an adjusted score vector and adjusted information matrix are found under an asymptotic development that holds as the leverages in the mean model become small. Subsequently, the expectation of the fitted deviances is obtained directly to show that the adjusted score vector is unbiased at least to,O(1/n). Exact results are obtained in the single-sample case. The results reduce to residual maximum likelihood estimation in the normal linear case. [source]

Semiclassical limit for the Schrödinger-Poisson equation in a crystal

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2001
Philippe Bechouche
We give a mathematically rigorous theory for the limit from a weakly nonlinear Schrödinger equation with both periodic and nonperiodic potential to the semiclassical version of the Vlasov equation. To this end we perform simultaneously a classical limit (vanishing Planck constant) and a homogenization limit of the periodic structure (vanishing lattice length taken proportional to the Planck constant). We introduce a new variant of Wigner transforms, namely the "Wigner Bloch series" as an adaption of the Wigner series for density matrices related to two different "energy bands." Another essential tool are estimates on the commutators of the projectors into the Floquet subspaces ("band subspaces") and the multiplicative potential operator that destroy the invariance of these band subspaces under the periodic Hamiltonian. We assume the initial data to be concentrated in isolated bands but allow for band crossing of the other bands which is the generic situation in more than one space dimension. The nonperiodic potential is obtained from a coupling to the Poisson equation, i.e., we take into account the self-consistent Coulomb interaction. Our results hold also for the easier linear case where this potential is given. We hence give the first rigorous derivation of the (nonlinear) "semiclassical equations" of solid state physics widely used to describe the dynamics of electrons in semiconductors. © 2001 John Wiley & Sons, Inc. [source]