Robust Small Sample Accurate Inference in Moment Condition Models

Procedures based on the Generalized Method of Moments (GMM) (Hansen, 1982) are basic tools in modern econometrics. In most cases, the theory available for making inference with these procedures is based on first order asymptotic theory. It is well-known that the (first order) asymptotic distribution does not provide accurate p-values and confidence intervals in moderate to small samples. Moreover, in the presence of small deviations from the assumed model, p-values and confidence intervals based on classical GMM procedures can be drastically affected (nonrobustness). Several alternative techniques have been proposed in the literature to improve the accuracy of GMM procedures. These alternatives address either the first order accuracy of the approximations (information and entropy econometrics (IEE)) or the nonrobustness (Robust GMM estimators and tests). In this paper, we propose a new alternative procedure which combines robustness properties and accuracy in small samples. Specifically, we combine IEE techniques as developed in Imbens, Spady, Johnson (1998) to obtain finite sample accuracy with robust methods obtained by bounding the original orthogonality function as proposed in Ronchetti and Trojani (2001). This leads to new robust estimators and tests in moment condition models with excellent finite sample accuracy. Finally, we illustrate the accuracy of the new statistic by means of some simulations for three models on overidentifying moment conditions.Exponential tilting, Generalized method of moments, Information and entropy econometrics, Monte Carlo, Robust tests, Saddlepoint techniques

Multibody Multipole Methods

A three-body potential function can account for interactions among triples of particles which are uncaptured by pairwise interaction functions such as Coulombic or Lennard-Jones potentials. Likewise, a multibody potential of order $n$ can account for interactions among $n$-tuples of particles uncaptured by interaction functions of lower orders. To date, the computation of multibody potential functions for a large number of particles has not been possible due to its $O(N^n)$ scaling cost. In this paper we describe a fast tree-code for efficiently approximating multibody potentials that can be factorized as products of functions of pairwise distances. For the first time, we show how to derive a Barnes-Hut type algorithm for handling interactions among more than two particles. Our algorithm uses two approximation schemes: 1) a deterministic series expansion-based method; 2) a Monte Carlo-based approximation based on the central limit theorem. Our approach guarantees a user-specified bound on the absolute or relative error in the computed potential with an asymptotic probability guarantee. We provide speedup results on a three-body dispersion potential, the Axilrod-Teller potential.Comment: To appear in Journal of Computational Physic

Estimation of the Handwritten Text Skew Based on Binary Moments

Binary moments represent one of the methods for the text skew estimation in binary images. It has been used widely for the skew identification of the printed text. However, the handwritten text consists of text objects, which are characterized with different skews. Hence, the method should be adapted for the handwritten text. This is achieved with the image splitting into separate text objects made by the bounding boxes. Obtained text objects represent the isolated binary objects. The application of the moment-based method to each binary object evaluates their local text skews. Due to the accuracy, estimated skew data can be used as an input to the algorithms for the text line segmentation

Silhouette-based gait recognition using Procrustes shape analysis and elliptic Fourier descriptors

This paper presents a gait recognition method which combines spatio-temporal motion characteristics, statistical and physical parameters (referred to as STM-SPP) of a human subject for its classification by analysing shape of the subject's silhouette contours using Procrustes shape analysis (PSA) and elliptic Fourier descriptors (EFDs). STM-SPP uses spatio-temporal gait characteristics and physical parameters of human body to resolve similar dissimilarity scores between probe and gallery sequences obtained by PSA. A part-based shape analysis using EFDs is also introduced to achieve robustness against carrying conditions. The classification results by PSA and EFDs are combined, resolving tie in ranking using contour matching based on Hu moments. Experimental results show STM-SPP outperforms several silhouette-based gait recognition methods

Gait recognition based on shape and motion analysis of silhouette contours

This paper presents a three-phase gait recognition method that analyses the spatio-temporal shape and dynamic motion (STS-DM) characteristics of a human subject’s silhouettes to identify the subject in the presence of most of the challenging factors that affect existing gait recognition systems. In phase 1, phase-weighted magnitude spectra of the Fourier descriptor of the silhouette contours at ten phases of a gait period are used to analyse the spatio-temporal changes of the subject’s shape. A component-based Fourier descriptor based on anatomical studies of human body is used to achieve robustness against shape variations caused by all common types of small carrying conditions with folded hands, at the subject’s back and in upright position. In phase 2, a full-body shape and motion analysis is performed by fitting ellipses to contour segments of ten phases of a gait period and using a histogram matching with Bhattacharyya distance of parameters of the ellipses as dissimilarity scores. In phase 3, dynamic time warping is used to analyse the angular rotation pattern of the subject’s leading knee with a consideration of arm-swing over a gait period to achieve identification that is invariant to walking speed, limited clothing variations, hair style changes and shadows under feet. The match scores generated in the three phases are fused using weight-based score-level fusion for robust identification in the presence of missing and distorted frames, and occlusion in the scene. Experimental analyses on various publicly available data sets show that STS-DM outperforms several state-of-the-art gait recognition methods

Molecular free path distribution in rarefied gases

We present the results of investigations into the distribution of molecular free paths in rarefied gases using molecular dynamics simulations. Our tests on a range of different gas densities and confinements (unbounded, single bounding wall and parallel bounding walls) indicate that the molecules perform Lévy-type flights, irrespective of the presence of a bounding wall. The free paths most closely follow a power-law distribution. Simulations of gases confined by planar surfaces indicate that the local molecular mean free path varies sharply close to a solid surface. These results may yield new insight into diffusive transport in rarefied gases, in particular, the constitutive behaviour of gas flows in micro- and nanoscale devices