# Numerical solution of robust regression problems: computational aspects, a comparison

Published on Jan 1, 1977in Journal of Statistical Computation and Simulation1.424

Â· DOI :10.1080/00949657708810152

Published on Jan 1, 1977in Journal of Statistical Computation and Simulation1.424

Â· DOI :10.1080/00949657708810152

References11

Newest

This disclosure is directed to a powered cutting tool and a cutting head adapted for use therewith comprising a housing for containing a motor means and an actuator for controlling the operation of the motor means. A cutting head is connected in driving relationship with the motor means. The cutting head includes a pair of relatively movable jaws having a by-pass disposed in substantial alignment with the shear line of the jaws so as to prohibit curling of the material or binding of the tool dur...

Maximum likelihood type robust estimates of regression are defined and their asymptotic properties are investigated both theoretically and empirically. Perhaps the most important new feature is that the number pof parameters is allowed to increase with the number nof observations. The initial terms of a formal power series expansion (essentially in powers of p/n show an excellent agreement with Monte Carlo results, in most cases down to 4 observations per parameter.

In recent years several algorithms have appeared for modifying the factors of a matrix following a rank-one change. These methods have always been given in the context of specific applications and this has probably inhibited their use over a wider field. In this report several methods are described for modifying Cholesky factors. Some of these have been published previously while others appear for the first time. In addition, a new algorithm is presented for modifying the complete orthogonal fac...

Let A be a real mÃ—n matrix with mâ‰§n. It is well known (cf. [4]) that $A = U\sum {V^T} (1) where {U^T}U = {V^T}V = V{V^T} = {I_n}{\text{ and }}\sum {\text{ = diag(}}{\sigma _{\text{1}}}{\text{,}} \ldots {\text{,}}{\sigma _n}{\text{)}}{\text{.}} The matrix U consists of n orthonormalized eigenvectors associated with the n largest eigenvalues of AA T , and the matrix V consists of the orthonormalized eigenvectors of A T A. The diagonal elements of âˆ‘ are the non-negative square roots of the e...

An Appraisal of Least Squares Programs for the Electronic Computer from the Point of View of the User

Abstract Although there are many linear least squares programs available for use on the electronic computer, the algorithms specified in many of these programs are numerically more appropriate for the desk calculator than for the electronic computer. Routines which may be efficient for desk calculators may not be efficient for electronic computers. Since most computers carry about eight digits in the calculations, routines which do not take the problem of round-off errors and truncation into acc...

This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimatorsâ€”intermediaries between sample mean and sample medianâ€”that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators. For the general background, see Tukey (1960) (p. 448 ff.)

Matrix Properties and Concepts.- Nonnegative Matrices.- Basic Iterative Methods and Comparison Theorems.- Successive Overrelaxation Iterative Methods.- Semi-Iterative Methods.- Derivation and Solution of Elliptic Difference Equations.- Alternating-Direction Implicit Iterative Methods.- Matrix Methods for Parabolic Partial Differential Equations.- Estimation of Acceleration Parameters.

A method for continuously effecting reactions in a liquid phase in the presence of a gas and of a finely divided solid catalyst in a bubble column-cascade reactor with little or no liquid back-mixing, dwell time in the reactor being dependent on the liquid and gas throughputs, said reactor comprising a vertical column and a plurality of equidistantly-spaced, horizontally mounted, uniformly-perforated plates therein, the aperture area of each plate being dependent on the cross-sectional area of t...

Cited By42

Newest

Abstract In this work a novel approach to estimate in situ the stress intensity factor (SIF) through the thickness of metal specimens is presented. It is based on a hybrid methodology that combines powerful synchrotron X-ray diffraction data with an elastic analytical model describing the strain field around the crack tip. A sensitivity analysis is conducted to understand the largest sources of error and their impact on the estimated SIF values. The accuracy in locating the crack tip position wa...

Unsupervised clustering of a set of datums into homogeneous groups is a primitive operation required in many signal and image processing applications. In fact, different incarnations and hybrids of Fuzzy C-Means (FCM) and Possibilistic C-means (PCM) have been suggested which address additional requirements such as accepting weighted sets and being robust to the presence of outliers. Nevertheless, arriving at a general framework, which is independent of the datum model and the notion of homogenei...

Unsupervised separation of a group of datums of a particular type, into clusters which are homogenous within a problem class-specific context, is a classical research problem which is still actively visited. Since the 1960s, the research community has converged into a class of clustering algorithms, which utilizes concepts such as fuzzy/probabilistic membership as well as possibilistic and credibilistic degrees. In spite of the differences in the formalizations and approaches to loss assessment ...

Given data yand kcovariates xthe problem is to decide which covariates to include when approximating yby a linear function of the covariates. The decision is based on replacing subsets of the covariates by i.i.d. normal random variables and comparing the error with that obtained by retaining the subsets. If the two errors are not significantly different for a particular subset it is concluded that the covariates in this subset are no better than random noise and they are not included...

The proposal ofMestimators for regression (Huber, 1973) and the development of an algorithm for its computation (Dutter, 1977) has lead to an increased activity for further research in this area. New regression estimators were introduced that combine a high level of robustness with high efficiency. Also fast algorithms have been developed and implemented in several software packages. We provide a review of the most important methods, and compare the performance of the algorithms implemented in R...

Data clustering is the generic process of splitting a set of datums into a number of homogenous sets. Nevertheless, although a clustering process inputs datums as a set of separate mathematical objects, these entities are in fact correlated within a spatial context specific to the problem class in hand. For example, when the data acquisition process yields a 2D matrix of regularly sampled measurements, as it is the case with image sensors which utilize different modalities, adjacent datums are h...

Regression based principal component analysis for sparse functional data with applications to screening growth paths

Growth charts are widely used in pediatric care for assessing childhood body size measurements (e.g., height or weight). The existing growth charts screen one body size at a single given age. However, when a child has multiple measures over time and exhibits a growth path, how to assess those measures jointly in a rigorous and quantitative way remains largely undeveloped in the literature. In this paper, we develop a new method to construct growth charts for growth paths. A new estimation algori...

This paper is motivated by the problem of local motion estimation via robust regression with linear models. In order to increase the robustness of the motion estimates, we propose a novel robust local optical flow approach based on a modified Hampel estimator. We show the deficiencies of the least squares estimator used by the standard Kanade-Lucas-Tomasi (KLT) tracker when the assumptions made by Lucas-Kanade are violated. We propose a strategy to adapt the window sizes to cope with the general...