Explosive Random‐Coefficient AR(1) Processes and Related Asymptotics for Least‐Squares Estimation

Abstract. Large sample properties of the least‐squares and weighted least‐squares estimates of the autoregressive parameter of the explosive random‐coefficient AR(1) process are discussed. It is shown that, contrary to the standard AR(1) case, the least‐squares estimator is inconsistent whereas the weighted least‐squares estimator is consistent and asymptotically normal even when the error process is not necessarily Gaussian. Conditional asymptotics on the event that a certain limiting random variable is non‐zero is also discussed.     

NEW APPROACH FOR ESTIMATION OF ΔJ AND FOR MEASUREMENT OF CRACK GROWTH AT ELEVATED TEMPERATURE

Abstract— The ACPD-method was used to measure crack growth in low cycle fatigue tests at elevated temperature. The material which was investigated at T = 550°C was the ferritic steel 2.25Cr–1Mo. Characteristic values of representative hysteresis loops were determined. The crack growth data were correlated with the effective part of the fracture mechanics parameter Δ J. A new method for the calculation of Δ J is proposed.     

A region-based selective optical flow back-projection for genuine motion vector estimation

Motion vector plays one significant feature in moving object segmentation. However, the motion vector in this application is required to represent the actual motion displacement, rather than regions of visually significant similarity. In this paper, region-based selective optical flow back-projection (RSOFB) which back-projects optical flows in a region to restore the region's motion vector from gradient-based optical flows, is proposed to obtain genuine motion displacement. The back-projection is performed based on minimizing the projection mean square errors of the motion vector on gradient directions. As optical flows of various magnitudes and directions provide various degrees of reliability in the genuine motion restoration, the optical flows to be used in the RSOFB are optimally selected based on their sensitivity to noises and their tendency in causing motion estimation errors. In this paper a deterministic solution is also derived for performing the minimization and obtaining the genuine motion magnitude and motion direction.     

Surface and normal ensembles for surface reconstruction

The majority of the existing techniques for surface reconstruction and the closely related problem of normal reconstruction are deterministic. Their main advantages are the speed and, given a reasonably good initial input, the high quality of the reconstructed surfaces. Nevertheless, their deterministic nature may hinder them from effectively handling incomplete data with noise and outliers. An ensemble is a statistical technique which can improve the performance of deterministic algorithms by putting them into a statistics based probabilistic setting. In this paper, we study the suitability of ensembles in normal and surface reconstruction. We experimented with a widely used normal reconstruction technique [Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W. Surface reconstruction from unorganized points. Computer Graphics 1992;71-8] and Multi-level Partitions of Unity implicits for surface reconstruction [Ohtake Y, Belyaev A, Alexa M, Turk G, Seidel H-P. Multi-level partition of unity implicits. ACM Transactions on Graphics 2003;22(3):463-70], showing that normal and surface ensembles can successfully be combined to handle noisy point sets.     

Generalized adaptive notch filters with frequency debiasing for tracking of polynomial phase systems

Generalized adaptive notch filters are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. For general patterns of frequency variation the generalized adaptive notch filtering algorithms yield biased frequency estimates. We show that when system frequencies change slowly in a smooth way, the estimation bias can be substantially reduced by means of post-filtering of the frequency estimates. The modified (debiased) algorithm has better tracking capabilities than the original algorithm.     

Cost estimation of structural skeleton using an interactive automation algorithm: A conceptual approach

This paper addresses a new concept for generating bills of quantities (B.o.Qs) using AutoCAD drawings for a building project, which demonstrates the application of Industry Foundation Class (IFC), developed by International Alliance for Interoperability (IAI). The procedure considers types of materials and the structural shapes of the AutoCAD drawings to compute the cost of the structural skeleton elements using interactive automation. The main concept focuses on using layer computation of the AutoCAD drawing after converting it into a drawing inter-exchangeable file format (DXF). Once the coordinates are detected, it is easier to determine the area and volume for any structural shape, including circles and polygons. The extracting method is a new technique for structural engineers and quantity surveyors to estimate required material for beam, columns, slabs and foundations. The algorithm extracts and recognizes the layers and objects from a two dimensional DXF drawing along with the coordinates information. The results obtained using this technique are more accurate and reliable than manual procedures or any other traditional techniques. In this paper, an automated and interactive procedure for B.o.Q computation is demonstrated. The process involves a user-friendly interface, dynamic linking to the structural drawings and tracking of B.o.Q modifications at the same time.     

Information cut for clustering using a gradient descent approach

We introduce a new graph cut for clustering which we call the Information Cut. It is derived using Parzen windowing to estimate an information theoretic distance measure between probability density functions. We propose to optimize the Information Cut using a gradient descent-based approach. Our algorithm has several advantages compared to many other graph-based methods in terms of determining an appropriate affinity measure, computational complexity, memory requirements and coping with different data scales. We show that our method may produce clustering and image segmentation results comparable or better than the state-of-the art graph-based methods.     

Robust estimation for circular data

The problems arising when there are outliers in a data set that follow a circular distribution are considered. A robust estimation of the unknown parameters is obtained using the methods of weighted likelihood and minimum disparity, each of which is defined for a general parametric family of circular data. The class of power divergence and the related residual adjustment function is investigated in order to improve the performance of the two methods which are studied for the Von Mises (circular normal) and the Wrapped Normal distributions. The techniques are illustrated via two examples based on a real data set and a Monte Carlo study, which also enables the discussion of various computational aspects.     

Consistency of robust estimators in multi-structural visual data segmentation

A theoretical framework is presented to study the consistency of robust estimators used in vision problems involving extraction of fine details. A strong correlation between asymptotic performance of a robust estimator and the asymptotic bias of its scale estimate is mathematically demonstrated where the structures are assumed to be linear corrupted by Gaussian noise. A new measure for the inconsistency of scale estimators is defined and formulated by deriving the functional forms of four recent high-breakdown robust estimators. For each estimator, the inconsistency measures are numerically evaluated for a range of mutual distances between structures and inlier ratios, and the minimum mutual distance between the structures, for which each estimator returns a non-bridging fit, is calculated.