An Approximation to the Optimal Subsample Allocation for Small Areas

Abstract

This paper develops allocation methods for stratified sample surveys in which small area estimation is a priority. We assume stratified sampling with small areas as the strata. Similar to Longford (2006), we seek efficient allocation that minimizes a linear combination of the mean squared errors of composite small area estimators and of an estimator of the overall mean. Unlike Longford, we define mean-squared error in a model-assisted framework, allowing a more natural interpretation of results using an intra-class correlation parameter. This allocation has an analytical form for a special case, and has the unappealing property that some strata may be allocated no sample. We derive a Taylor approximation to the stratum sample sizes for small area estimation using composite estimation giving priority to both small area and national estimation.

Designing 3D topological insulators by 2D-Xene (X = Ge, Sn) sheet functionalization in GaGeTe-type structures

“…Herewith, we suggest a new platform for 3D strong topological insulators: GaGeTe-type layered bulk materials that are structurally related to both basic zincblendetype semiconductors and 2D-Xene materials. 7 The progenitor GaGeTe has been synthesized as bulk crystals. 8,9 It has a layered crystal structure stacked from sixatom-thick 2 N [Te-Ga-Ge-Ge-Ga-Te] building blocks (denoted henceforward as a hextuple layer of GaGeTe) separated by van der Waals gaps.…”

“…These artificial 2D materials coined Xenes (X = IVA elements), which accommodate X atoms in the buckled honeycomb arrangement, are predicted to exhibit the quantum spin Hall effect (QSHE), possibly even persisting up to room temperature. 7 Furthermore, some proposals advocate that topological states emerge in the covalently functionalized Xane derivatives. For instance, a 2D topological insulator is expected in halogenfunctionalized germanane GeX (X = H, F, Cl, Br), methylsubstituted GeCH 3 16-18 and ethynyl derivatives of germanene GeC 2 X (X = H, halogen) 19 under sizeable tensile strain.…”

Topological Phase Transitions in the Photonic Spin Hall Effect

“…It exhibits a unique potential for applications in precision metrology, including bio-sensing [7], nanoprobing [8], and thin films and multilayer graphene characterization [9][10][11]. It has also been used to identify different absorption mechanisms in bulk semiconductors [12,13].Staggered two-dimensional semiconductors [14][15][16], including silicene [17], germanene [18], and stanene [19,20] are monolayer materials made of Silicon, Germanium, and Tin atoms, respectively, arranged in a honeycomb lattice. Unlike graphene [21], these materials are nonplanar and possess intrinsic spin-orbit coupling that results in the opening of a gap in their electronic band structure.…”

“…Staggered two-dimensional semiconductors [14][15][16], including silicene [17], germanene [18], and stanene [19,20] are monolayer materials made of Silicon, Germanium, and Tin atoms, respectively, arranged in a honeycomb lattice. Unlike graphene [21], these materials are nonplanar and possess intrinsic spin-orbit coupling that results in the opening of a gap in their electronic band structure.…”

“…Given the reported sensitivities for measuring the SHEL through weak measurement approaches [5], we conclude that an experimental demonstration of our results is within current capabilities. In spite of the fast experimental progress in the synthesis of staggered materials of the graphene family [14][15][16][17][18][19][20] suggests that they will be easily accessible in the near future, some of our results can be tested in graphene, as it presents topological insulator features under circularly polarized illumination (only QSHI and AQHI phases can be probed in this case) [39]. We envision the effects predicted here will greatly impact research in spinoptics, spintronics, and valleytronics.…”