Identifiability of Normal and Normal Mixture Models With Nonignorable Missing Data

Missing data problems arise in many applied research studies. They may jeopardize statistical inference of the model of interest, if the missing mechanism is nonignorable, that is, the missing mechanism depends on the missing values themselves even conditional on the observed data. With a nonignorable missing mechanism, the model of interest is often not identifiable without imposing further assumptions. We find that even if the missing mechanism has a known parametric form, the model is not identifiable without specifying a parametric outcome distribution. Although it is fundamental for valid statistical inference, identifiability under nonignorable missing mechanisms is not established for many commonly-used models. In this paper, we first demonstrate identifiability of the normal distribution under monotone missing mechanisms. We then extend it to the normal mixture and $t$ mixture models with non-monotone missing mechanisms. We discover that models under the Logistic missing mechanism are less identifiable than those under the Probit missing mechanism. We give necessary and sufficient conditions for identifiability of models under the Logistic missing mechanism, which sometimes can be checked in real data analysis. We illustrate our methods using a series of simulations, and apply them to a real-life dataset

Towards Constraining Parity-Violations in Gravity with Satellite Gradiometry

Parity violation in gravity, if existed, could have important implications, and it is meaningful to search and test the possible observational effects. Chern-Simons modified gravity serves as a natural model for gravitational parity-violations. Especially, considering extensions to Einstein-Hilbert action up to second order curvature terms, it is known that theories of gravitational parity-violation will reduce to the dynamical Chern-Simons gravity. In this letter, we outline the theoretical principles of testing the dynamical Chern-Simons gravity with orbiting gravity gradiometers, which could be naturally incorporated into future satellite gravity missions. The secular gravity gradient signals, due to the Mashhoon-Theiss (anomaly) effect, in dynamical Chern-Simons gravity are worked out, which can improve the constraint of the corresponding Chern-Simons length scale $\xi^{\frac{1}{4}}_{cs}$ obtained from such measurement scheme. For orbiting superconducting gradiometers or gradiometers with optical readout, a bound $\xi^{\frac{1}{4}}_{cs}\leq 10^6 \ km$ (or even better) could in principle be obtained, which will be at least 2 orders of magnitude stronger than the current one based on the observations from the GP-B mission and the LAGEOS I, II satellites.Comment: 15 pages, 6 figures. arXiv admin note: text overlap with arXiv:1606.0818

Characterizing the Dynamic Response of a Chassis Frame in a Heavy-Duty Dump Vehicle based on an Improved Stochastic System Identification

This paper presents an online method for the assessment of the dynamic performance of the chassis frame in a heavy-duty dump truck based on a novel stochastic subspace identification (SSI) method. It introduces the use of an average correlation signal as the input data to conventional SSI methods in order to reduce the noisy and nonstationary contents in the vibration signals from the frame, allowing accurate modal properties to be attained for realistically assessing the dynamic behaviour of the frame when the vehicle travels on both bumped and unpaved roads under different operating conditions. The modal results show that the modal properties obtained online are significantly different from the offline ones in that the identifiable modes are less because of the integration of different vehicle systems onto the frame. Moreover, the modal shapes between 7Hz and 40Hz clearly indicate the weak section of the structure where earlier fatigues and unsafe operations may occur due to the high relative changes in the modal shapes. In addition, the loaded operations show more modes which cause high deformation on the weak section. These results have verified the performance of the proposed SSI method and provide reliable references for optimizing the construction of the frame

The relationship of electron Fermi energy with strong magnetic fields

In order to depict the quantization of Landau levels, we introduce Dirac $\delta$ function, and gain a concise expression for the electron Fermi energy, $E_{F}(e) \propto B^{1/4}$. The high soft X-ray luminosities of magnetars may be naturally explained by our theory.Comment: 3 pages, 1 figure, submitted to OMEG11 Proceeding (Tokyo, Japan. Nov.14-18, 2011