A pseudo empirical likelihood approach for stratified samples with nonresponse

Nonresponse is common in surveys. When the response probability of a survey variable $Y$ depends on $Y$ through an observed auxiliary categorical variable $Z$ (i.e., the response probability of $Y$ is conditionally independent of $Y$ given $Z$), a simple method often used in practice is to use $Z$ categories as imputation cells and construct estimators by imputing nonrespondents or reweighting respondents within each imputation cell. This simple method, however, is inefficient when some $Z$ categories have small sizes and ad hoc methods are often applied to collapse small imputation cells. Assuming a parametric model on the conditional probability of $Z$ given $Y$ and a nonparametric model on the distribution of $Y$, we develop a pseudo empirical likelihood method to provide more efficient survey estimators. Our method avoids any ad hoc collapsing small $Z$ categories, since reweighting or imputation is done across $Z$ categories. Asymptotic distributions for estimators of population means based on the pseudo empirical likelihood method are derived. For variance estimation, we consider a bootstrap procedure and its consistency is established. Some simulation results are provided to assess the finite sample performance of the proposed estimators.Comment: Published in at http://dx.doi.org/10.1214/07-AOS578 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Aspect ratio dependence of heat transport by turbulent Rayleigh-B\'{e}nard convection in rectangular cells

We report high-precision measurements of the Nusselt number $Nu$ as a function of the Rayleigh number $Ra$ in water-filled rectangular Rayleigh-B\'{e}nard convection cells. The horizontal length $L$ and width $W$ of the cells are 50.0 cm and 15.0 cm, respectively, and the heights $H=49.9$, 25.0, 12.5, 6.9, 3.5, and 2.4 cm, corresponding to the aspect ratios $(\Gamma_x\equiv L/H,\Gamma_y\equiv W/H)=(1,0.3)$, $(2,0.6)$, $(4,1.2)$, $(7.3,2.2)$, $(14.3,4.3)$, and $(20.8,6.3)$. The measurements were carried out over the Rayleigh number range $6\times10^5\lesssim Ra\lesssim10^{11}$ and the Prandtl number range $5.2\lesssim Pr\lesssim7$. Our results show that for rectangular geometry turbulent heat transport is independent of the cells' aspect ratios and hence is insensitive to the nature and structures of the large-scale mean flows of the system. This is slightly different from the observations in cylindrical cells where $Nu$ is found to be in general a decreasing function of $\Gamma$, at least for $\Gamma=1$ and larger. Such a difference is probably a manifestation of the finite plate conductivity effect. Corrections for the influence of the finite conductivity of the top and bottom plates are made to obtain the estimates of $Nu_{\infty}$ for plates with perfect conductivity. The local scaling exponents $\beta_l$ of $Nu_{\infty}\sim Ra^{\beta_l}$ are calculated and found to increase from 0.243 at $Ra\simeq9\times10^5$ to 0.327 at $Ra\simeq4\times10^{10}$.Comment: 15 pages, 7 figures, Accepted by Journal of Fluid Mechanic

Learning Fully Dense Neural Networks for Image Semantic Segmentation

Semantic segmentation is pixel-wise classification which retains critical spatial information. The "feature map reuse" has been commonly adopted in CNN based approaches to take advantage of feature maps in the early layers for the later spatial reconstruction. Along this direction, we go a step further by proposing a fully dense neural network with an encoder-decoder structure that we abbreviate as FDNet. For each stage in the decoder module, feature maps of all the previous blocks are adaptively aggregated to feed-forward as input. On the one hand, it reconstructs the spatial boundaries accurately. On the other hand, it learns more efficiently with the more efficient gradient backpropagation. In addition, we propose the boundary-aware loss function to focus more attention on the pixels near the boundary, which boosts the "hard examples" labeling. We have demonstrated the best performance of the FDNet on the two benchmark datasets: PASCAL VOC 2012, NYUDv2 over previous works when not considering training on other datasets

Diagnostic accuracy of cardiovascular magnetic resonance for patients with suspected cardiac amyloidosis: a systematic review and meta-analysis

Search strategy. (DOCX 142 kb