Variable selection in nonparametric additive models

We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is "small" relative to the sample size. The statistical problem is to determine which additive components are nonzero. The additive components are approximated by truncated series expansions with B-spline bases. With this approximation, the problem of component selection becomes that of selecting the groups of coefficients in the expansion. We apply the adaptive group Lasso to select nonzero components, using the group Lasso to obtain an initial estimator and reduce the dimension of the problem. We give conditions under which the group Lasso selects a model whose number of components is comparable with the underlying model, and the adaptive group Lasso selects the nonzero components correctly with probability approaching one as the sample size increases and achieves the optimal rate of convergence. The results of Monte Carlo experiments show that the adaptive group Lasso procedure works well with samples of moderate size. A data example is used to illustrate the application of the proposed method.Comment: Published in at http://dx.doi.org/10.1214/09-AOS781 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

From Poincaré Inequalities to Nonlinear Matrix Concentration

This paper deduces exponential matrix concentration from a Poincaré inequality via a short, conceptual argument. Among other examples, this theory applies to matrix-valued functions of a uniformly log-concave random vector. The proof relies on the subadditivity of Poincaré inequalities and a chain rule inequality for the trace of the matrix Dirichlet form. It also uses a symmetrization technique to avoid difficulties associated with a direct extension of the classic scalar argument

Pressure dependence of magnetic ordering temperature for decamethylferrocenium tetracyanoethenide

Journal ArticleIt has been demonstrated that the linear-chain charge-transfer salt, decamethylferrocenium tetracyanoethanide (DMeFc) (TCNE), is a ferromagnet with a transition temperature of -4.8 K. This low-temperature 3D ordering has been attributed to a strong intrachain and a weak interchain interaction. To study these interactions, we have determined the Tc up to 20 kbar by measuring the ac susceptibility (X) at low frequency. Our results show that the Tc increases with pressure at a rate of -0.22 K/kbar, while the (X) peak indicative of the ferromagnetic transition continues to decrease rapidly. A small peak was also detected above the main transition at pressures above 3 kbar. This new peak persists even after the pressure is removed. The result from dc magnetization suggests that this corresponds to a metamagnetic state. For the first time, we have observed pressure-induced phase-transition in this material