On the approximate maximum likelihood estimation for diffusion processes

The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. A\"{\i}t-Sahalia [J. Finance 54 (1999) 1361--1395; Econometrica 70 (2002) 223--262] proposed asymptotic expansions to the transition densities of diffusion processes, which lead to an approximate maximum likelihood estimation (AMLE) for parameters. Built on A\"{\i}t-Sahalia's [Econometrica 70 (2002) 223--262; Ann. Statist. 36 (2008) 906--937] proposal and analysis on the AMLE, we establish the consistency and convergence rate of the AMLE, which reveal the roles played by the number of terms used in the asymptotic density expansions and the sampling interval between successive observations. We find conditions under which the AMLE has the same asymptotic distribution as that of the full MLE. A first order approximation to the Fisher information matrix is proposed.Comment: Published in at http://dx.doi.org/10.1214/11-AOS922 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Abnormality Detection in Mammography using Deep Convolutional Neural Networks

Breast cancer is the most common cancer in women worldwide. The most common screening technology is mammography. To reduce the cost and workload of radiologists, we propose a computer aided detection approach for classifying and localizing calcifications and masses in mammogram images. To improve on conventional approaches, we apply deep convolutional neural networks (CNN) for automatic feature learning and classifier building. In computer-aided mammography, deep CNN classifiers cannot be trained directly on full mammogram images because of the loss of image details from resizing at input layers. Instead, our classifiers are trained on labelled image patches and then adapted to work on full mammogram images for localizing the abnormalities. State-of-the-art deep convolutional neural networks are compared on their performance of classifying the abnormalities. Experimental results indicate that VGGNet receives the best overall accuracy at 92.53\% in classifications. For localizing abnormalities, ResNet is selected for computing class activation maps because it is ready to be deployed without structural change or further training. Our approach demonstrates that deep convolutional neural network classifiers have remarkable localization capabilities despite no supervision on the location of abnormalities is provided.Comment: 6 page

Hidden force opposing ice compression

Coulomb repulsion between the unevenly-bound bonding and nonbonding electron pairs in the O:H-O hydrogen-bond is shown to originate the anomalies of ice under compression. Consistency between experimental observations, density functional theory and molecular dynamics calculations confirmed that the resultant force of the compression, the repulsion, and the recovery of electron-pair dislocations differentiates ice from other materials in response to pressure. The compression shortens and strengthens the longer-and-softer intermolecular O:H lone-pair virtual-bond; the repulsion pushes the bonding electron pair away from the H+/p and hence lengthens and weakens the intramolecular H-O real-bond. The virtual-bond compression and the real-bond elongation symmetrize the O:H-O as observed at ~60 GPa and result in the abnormally low compressibility of ice. The virtual-bond stretching phonons (< 400 cm-1) are thus stiffened and the real-bond stretching phonons (> 3000 cm-1) softened upon compression. The cohesive energy of the real-bond dominates and its loss lowers the critical temperature for the VIII-VII phase transition. The polarization of the lone electron pairs and the entrapment of the bonding electron pairs by compression expand the band gap consequently. Findings should form striking impact to understanding the physical anomalies of H2O.Comment: arXiv admin note: text overlap with arXiv:1110.007

The dependence of tidal stripping efficiency on the satellite and host galaxy morphology

In this paper we study the tidal stripping process for satellite galaxies orbiting around a massive host galaxy, and focus on its dependence on the morphology of both satellite and host galaxy. For this purpose, we use three different morphologies for the satellites: pure disc, pure bulge and a mixture bulge+disc. Two morphologies are used for the host galaxies: bulge+disc and pure bulge. We find that while the spheroidal stellar component experiences a constant power-law like mass removal, the disc is exposed to an exponential mass loss when the tidal radius of the satellite is of the same order of the disc scale length. This dramatic mass loss is able to completely remove the stellar component on time scale of 100 Myears. As a consequence two satellites with the same stellar and dark matter masses, on the same orbit could either retain considerable fraction of their stellar mass after 10 Gyrs or being completely destroyed, depending on their initial stellar morphology. We find that there are two characteristic time scales describing the beginning and the end of the disc removal, whose values are related to the size of the disc. This result can be easily incorporated in semi-analytical models. We also find that the host morphology and the orbital parameters also have an effect on the determining the mass removal, but they are of secondary importance with respect to satellite morphology. We conclude that satellite morphology has a very strong effect on the efficiency of stellar stripping and should be taken into account in modeling galaxy formation and evolution.Comment: 11 pages, 9 figures; accepted for publication in MNRA

High dimensional generalized empirical likelihood for moment restrictions with dependent data

This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and the parameters diverge along with the sample size. The consistency with rates and the asymptotic normality of the GEL estimator are obtained by properly restricting the growth rates of the dimensions of the parameters and the moment restrictions, as well as the degree of data dependence. It is shown that even in the high dimensional time series setting, the GEL ratio can still behave like a chi-square random variable asymptotically. A consistent test for the over-identification is proposed. A penalized GEL method is also provided for estimation under sparsity setting