This article examines the construction of aggregation functions from data by minimizing the least absolute deviation criterion. We formulate various instances of such problems as linear programming problems. We consider the cases in which the data are provided as intervals, and the outputs ordering needs to be preserved, and show that linear programming formulation is valid for such cases. This...

Least absolute deviation (LAD) regression is an important tool used in numerous applications throughout science and engineering, mainly due to the intrinsic robust characteristics of LAD. In this paper, we show that the optimization needed to solve the LAD regression problem can be viewed as a sequence of maximum likelihood estimates (MLE) of location. The derived algorithm reduces to an iterat...

We report the discovery of a large-scale structure of Lyman α emitters (LAEs) at z = 4.86 based on widefield imaging with the prime-focus camera (Suprime-Cam) on the Subaru telescope. We observed a 25 × 45 area of the Subaru Deep Field in a narrow band (NB711, λC = 7126Å and FWHM= 73Å) together with R and i. We isolate from these data 43 LAE candidates down to NB711 = 25.5 mag using color crite...

For testing a linear hypothesis in a censored regression (or censored “Tobit”) model, three test criteria and four test statistics based on least absolute deviations estimates of parameters are proposed and their limiting chi-square distributions are established. Some consistent estimates of nuisance parameters are obtained for use in computing the test statistics. A simulation study for small ...

This article suggests very simple three-step estimators for censored quantile regression models with a separation restriction on the censoring probability. The estimators are theoretically attractive (i.e., asymptotically as efŽ cient as the celebrated Powell’s censored least absolute deviation estimator). At the same time, they are conceptually simple and have trivial computational expenses. T...

Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed covariates than methods such as least-squares or least absolute deviations regression. It can be expressed as a linear program, and, with appropriate preprocessing, i...

This article examines the impact of cognitive skills on the income of households in Ghana. It uses scores on mathematics and English tests to measure cognitive skills and estimates the returns to these skills based on farm profit, off-farm income, and total income. The article uses Powell’s censored least absolute deviations and symmetrically trimmed least squares estimators to estimate farm an...

This note considers some aspects of the computational problem of by minimizing the sum of absolute deviations Yt = t 1 x· t l3· l= l l fitting the regression model (t = 1, 2, ... , n) r!: 1 x· t l3·1 l= l l The iterative method recently proposed by Schlossmacher (1973) is shown to have undesirable features under certain conditions. The linear programming approach using the simplex method as sug...

This note considers some aspects of the computational problem of k fitting the regression model Yt ~ ti~l Xit~i +~t (t ~ 1, 2, ... , n) by minimizing the sum of absolute deviations ~~lIYt ~=l Xit~il The iterative method recently proposed by Schlossmacher (1973) is shown to have undesirable features under certain conditions. The linear programming approach using the simplex method as suggested b...

Original scientific paper The paper sets out to describe the results obtained by investigating the prediction of technological parameters and, indirectly, of technological time needed for seam tube polishing. The results of experimental investigations were used to define, analyse and compare two models. One is a mathematical i.e. statistical model obtained by the application of the least square...