Variable selection by searching for good subsets

Machine learning and statistical models are increasingly used in a prediction context and in the process of building these models the question of which variables to include often arises. Over the last 50 years a number of procedures have been proposed, especially in the statistical literature. In this paper a newvariable selection procedure is introduced for linear models. A subset of variables is defined here to be “good at margin λ” if it has two properties, namely (i) its associated criterion of fit will be improved in relative terms by less than λ if any variable is added to it, and (ii) its criterion of fit will deteriorate in relative terms by at least λ if any variable inside it, is dropped from it. Thus, such a subset contains all variables that are individually important and none that are unimportant at a given margin λ ≥ 0. This paper discusses calculation of such λ-good subsets. The “good” approach extends readily to generalised linear and many other models by using an appropriate criterion of performance. The approach is illustrated on an artificial data set and a number of real data sets

A framework for normal mean variance mixture innovations with application to GARCH modelling

GARCH models are useful to estimate the volatility of financial return series. Historically the innovation distribution of a GARCH model was assumed to be standard normal but recent research emphasizes the need for more general distributions allowing both asymmetry (skewness) and kurtosis in the innovation distribution to obtain better fitting models. A number of authors have proposed models which are special cases of the class of normal mean variance mixtures. We introduce a general framework within which this class of innovation distributions may be discussed. This entails writing the innovation term as a standardised combination of two variables, namely a normally distributed term and a mixing variable, each with its own interpretation. We list the existing models that fit into this framework and compare the corresponding innovation distributions, finding that they tend to be quite similar. This is confirmed by an empirical illustration which fits the models to the monthly excess returns series of the US stocks. The illustration finds further support for the ICAPM model of Merton, thus supporting recent results of Lanne and Saikonnen (2006)

Superconductivity in a Molecular Metal Cluster Compound

Compelling evidence for band-type conductivity and even bulk superconductivity below $T\_{\text{c}}\approx 8$ K has been found in $^{69,71}$Ga-NMR experiments in crystalline ordered, giant Ga$\_{84}$ cluster-compounds. This material appears to represent the first realization of a theoretical model proposed by Friedel in 1992 for superconductivity in ordered arrays of weakly coupled, identical metal nanoparticles.Comment: 5 pages, 4 figure

Muon Spin Relaxation Studies of Superconductivity in a Crystalline Array of Weakly Coupled Metal Nanoparticles

We report Muon Spin Relaxation studies in weak transverse fields of the superconductivity in the metal cluster compound, Ga$\_{84}$[N(SiMe$\_{3}$)$\_{2}$]$\_{20}$-Li$\_{6}$Br$\_{2}$(thf)$\_{20}\cdot$2toluene. The temperature and field dependence of the muon spin relaxation rate and Knight shift clearly evidence type II bulk superconductivity below $T\_{\text{c}}\approx7.8$ K, with $B\_{\text{c1}}\approx 0.06$ T, $B\_{\text{c2}}\approx 0.26$ T, $\kappa\sim 2$ and weak flux pinning. The data are well described by the s-wave BCS model with weak electron-phonon coupling in the clean limit. A qualitative explanation for the conduction mechanism in this novel type of narrow band superconductor is presented.Comment: 4 figures, 5 page

Magnetic dipolar ordering and relaxation in the high-spin molecular cluster compound Mn6

Few examples of magnetic systems displaying a transition to pure dipolar magnetic order are known to date, and single-molecule magnets can provide an interesting example. The molecular cluster spins and thus their dipolar interaction energy can be quite high, leading to reasonably accessible ordering temperatures, provided the crystal field anisotropy is sufficiently small. This condition can be met for molecular clusters of sufficiently high symmetry, as for the Mn6 compound studied here. Magnetic specific heat and susceptibility experiments show a transition to ferromagnetic dipolar order at T_{c} = 0.16 K. Classical Monte-Carlo calculations indeed predict ferromagnetic ordering and account for the correct value of T_{c}. In high magnetic fields we detected the contribution of the ^{55}Mn nuclei to the specific heat, and the characteristic timescale of nuclear relaxation. This was compared with results obtained directly from pulse-NMR experiments. The data are in good mutual agreement and can be well described by the theory for magnetic relaxation in highly polarized paramagnetic crystals and for dynamic nuclear polarization, which we extensively review. The experiments provide an interesting comparison with the recently investigated nuclear spin dynamics in the anisotropic single molecule magnet Mn12-ac.Comment: 19 pages, 11 eps figures. Contains extensive discussions on dipolar ordering, specific heat and nuclear relaxation in molecular magnet

Spin Stiffness in the Hubbard model

The spin stiffness $\rho_{\rm s}$ of the repulsive Hubbard model that occurs in the hydrodynamic theory of antiferromagnetic spin waves is shown to be the same as the thermodynamically defined stiffness involved in twisting the order parameter. New expressions for $\rho_{\rm s}$ are derived, which enable easier interpretation, and connections with superconducting weight and gauge invariance are discussed.Comment: 21 Pages LaTeX2e, to be published in Journal of Physics