Search results for "Statistics::Theory"
showing 6 items of 56 documents
On the ambiguous consequences of omitting variables
2015
This paper studies what happens when we move from a short regression to a long regression (or vice versa), when the long regression is shorter than the data-generation process. In the special case where the long regression equals the data-generation process, the least-squares estimators have smaller bias (in fact zero bias) but larger variances in the long regression than in the short regression. But if the long regression is also misspecified, the bias may not be smaller. We provide bias and mean squared error comparisons and study the dependence of the differences on the misspecification parameter.
Ordering and demixing transitions in multicomponent Widom-Rowlinson models.
1995
We use Monte Carlo techniques and analytical methods to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M between two and six there is a direct transition from the gas phase at z < z_d (M) to a demixed phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In this phase, which is driven by entropy, particles, independent of species, preferentially occupy one of the sublattices, i.e. spatial symmetry but not …
On the sign recovery by LASSO, thresholded LASSO and thresholded Basis Pursuit Denoising
2020
Basis Pursuit (BP), Basis Pursuit DeNoising (BPDN), and LASSO are popular methods for identifyingimportant predictors in the high-dimensional linear regression model Y = Xβ + ε. By definition, whenε = 0, BP uniquely recovers β when Xβ = Xb and β different than b implies L1 norm of β is smaller than the L1 norm of b (identifiability condition). Furthermore, LASSO can recover the sign of β only under a much stronger irrepresentability condition. Meanwhile, it is known that the model selection properties of LASSO can be improved by hard-thresholdingits estimates. This article supports these findings by proving that thresholded LASSO, thresholded BPDNand thresholded BP recover the sign of β in …
Intensity of theB1gphonon Raman scattering inYBa2Cu3O7: Comparison of normal and superconducting states
1995
We compare theoretically the intensity of the ${\mathit{B}}_{1\mathit{g}}$ phonon Raman scattering in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ above and below the superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$. Our analysis shows that a considerable enhancement of the scattering intensity in the superconducting state that is observed experimentally can be caused by an extension of the number of intermediate electronic states near the Fermi surface that participate in the Raman process.
Critical behavior of the surface-layer magnetization at the extraordinary transition in the three-dimensional Ising model.
1990
We have used a vectorized multispin-coding Monte Carlo method to determine the behavior of the surface-layer magnetization ${\mathit{m}}_{1}$ at the bulk transition in a simple-cubic Ising film with strongly enhanced surface coupling, i.e., at the extraordinary transition. In contrast to recent renormalization-group calculations we find no evidence for a discontinuous slope in the temperature dependence of ${\mathit{m}}_{1}$; the data are consistent with a free-energy-like (T-${\mathit{T}}_{\mathit{c}}$${)}^{2\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$ behavior plus background terms.
Game-Theoretic Approach to Hölder Regularity for PDEs Involving Eigenvalues of the Hessian
2021
AbstractWe prove a local Hölder estimate for any exponent $0<\delta <\frac {1}{2}$ 0 < δ < 1 2 for solutions of the dynamic programming principle $$ \begin{array}{@{}rcl@{}} u^{\varepsilon} (x) = \sum\limits_{j=1}^{n} \alpha_{j} \underset{\dim(S)=j}{\inf} \underset{|v|=1}{\underset{v\in S}{\sup}} \frac{u^{\varepsilon} (x + \varepsilon v) + u^{\varepsilon} (x - \varepsilon v)}{2} \end{array} $$ u ε ( x ) = ∑ j = 1 n α j inf dim ( S ) = j sup v ∈ S | v | = 1 u ε ( x + ε v ) + u ε ( x − ε v ) 2 with α1,αn > 0 and α2,⋯ ,αn− 1 ≥ 0. The proof is based on a new coupling idea from game theory. As an application, we get the same regularity estimate for viscosity solutions of the PDE $…