Asymptotics for sliced average variance estimation

In this paper, we systematically study the consistency of sliced average variance estimation (SAVE). The findings reveal that when the response is continuous, the asymptotic behavior of SAVE is rather different from that of sliced inverse regression (SIR). SIR can achieve $\sqrt{n}$ consistency even when each slice contains only two data points. However, SAVE cannot be $\sqrt{n}$ consistent and it even turns out to be not consistent when each slice contains a fixed number of data points that do not depend on n, where n is the sample size. These results theoretically confirm the notion that SAVE is more sensitive to the number of slices than SIR. Taking this into account, a bias correction is recommended in order to allow SAVE to be $\sqrt{n}$ consistent. In contrast, when the response is discrete and takes finite values, $\sqrt{n}$ consistency can be achieved. Therefore, an approximation through discretization, which is commonly used in practice, is studied. A simulation study is carried out for the purposes of illustration.Comment: Published at http://dx.doi.org/10.1214/009053606000001091 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Naturalness, dark matter, and the muon anomalous magnetic moment in supersymmetric extensions of the standard model with a pseudo-Dirac gluino

We study the naturalness, dark matter, and muon anomalous magnetic moment in the Supersymmetric Standard Models (SSMs) with a pseudo-Dirac gluino (PDGSSMs) from hybrid $F-$ and $D-$term supersymmetry (SUSY) breakings. To obtain the observed dark matter relic density and explain the muon anomalous magnetic moment, we find that the low energy fine-tuning measures are larger than about 30 due to strong constraints from the LUX and PANDAX experiments. Thus, to study the natural PDGSSMs, we consider multi-component dark matter and then the relic density of the lighest supersymmetric particle (LSP) neutralino is smaller than the correct value. We classify our models into six kinds: (i) Case A is a general case, which has small low energy fine-tuning measure and can explain the anomalous magnetic moment of the muon; (ii) Case B with the LSP neutralino and light stau coannihilation; (iii) Case C with Higgs funnel; (iv) Case D with Higgsino LSP; (v) Case E with light stau coannihilation and Higgsino LSP; (vi) Case F with Higgs funnel and Higgsino LSP. We study these Cases in details, and show that our models can be natural and consistent with the LUX and PANDAX experiments, as well as explain the muon anomalous magnetic moment. In particular, all these cases except the stau coannihilation can even have low energy fine-tuning measures around 10.Comment: 19 pages, 18 figure

Topological Semimetal-Insulator Quantum Phase Transition in Zintl Compounds Ba2X (X=Si, Ge)

By first-principles calculations, we find that Ba2X(X=Si, Ge) hosts a topological semimetal phase with one nodal ring in the kx=0 plane, which is protected by the glide mirror symmetry when spin-orbit coupling (SOC) is ignored. The corresponding drumheadlike surface flat band appears on the (100) surface in surface Green function calculation. Furthermore, a topological-semimetal-to-insulator transition (TSMIT) is found. The nodal line semimetal would evolve into topological insulator as SOC is turned on. The topologically protected metallic surface states emerge around the Gamma=0 point, which could be tuned into topologically-trivial insulator state by more than 3% hydrostatic strain. These results reveal a new category of materials showing quantum phase transition between topological semimetal and insulator, and tunability through elastic strain engineering.Comment: 14 pages. 4 figure