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

Trade Liberalization and Trade Performance of Environmental Goods: Evidence from Asia-Pacific Economic Cooperation Members

In this article, we study the impact of trade liberalization, including reductions in both tariff and nontariff trade barriers, on environmental goods (EGs) exports. Using bilateral trade data from 20 Asia-Pacific Economic Cooperation members, we find that tariff reduction in an exporting country has a larger positive impact on its exports of EGs than tariff reduction in an importing country. Our results also show that a lower nontariff barrier in an importing country increases its imports of EGs. A considerable amount of heterogeneity also exists in subsample results based on countries’ income levels

Dark Energy and Normalization of the Cosmological Wave Function

Dark energy is investigated from the perspective of quantum cosmology. It is found that, together with an appropriate normal ordering factor $q$, only when there is dark energy then can the cosmological wave function be normalized. This interesting observation may require further attention.Comment: Title changed, match the published versio

Study on Seismic Dynamic Response of Shallow-Buried Subway Station Structure and Ancillary Facilities

Strong earthquakes can cause damages to structural members and also yield non-negligible damages to nonstructural facilities, the latter being closely related to earthquake-induced inertial forces. At present, the acceleration response regularity of shallow-buried subway station structure is not very clear. Using the finite-element software ABAQUS, a dynamic soil-structure interaction model for a two-story subway station structure is established. The distribution of the peak acceleration response of the structure is obtained, and the damage assessment of non-structural facilities is carried out based on the structural acceleration response. The results demonstrate that, in general, the peak acceleration responses of the subway station structure increase from lower to upper story levels, while the peak acceleration responses at the same height are practically equal. Moreover, the peak accelerations of a shallow-buried subway station structure are generally less than or close to the peak ground acceleration. Furthermore, the nonstructural facilities are slightly damaged when subjected to a peak bedrock input acceleration of 0.1 g, and moderately damaged under a peak bedrock input acceleration in the range 0.2 – 0.6 g. Based on the acceleration response characteristics, it is proposed that the peak surface acceleration can be used as an index to evaluate the damage of non-structural facilities in shallow-buried subway station structure, which is simple, practical and basically meets the precision requirements