Showing papers on "Unit-weighted regression published in 1992"
TL;DR: In this article, regression quantiles and regression rank-scores are computed as solutions of a linear programming problem, and the solutions of the corresponding dual problem, which are called the regression rankscores, generalize the duality of order statistics and of ranks from the location to the linear model.
Abstract: We show that regression quantiles, which could be computed as solutions of a linear programming problem, and the solutions of the corresponding dual problem, which we call the regression rank-scores, generalize the duality of order statistics and of ranks from the location to the linear model. Noting this fact, we study the regression quantile and regression rank-score processes in the heteroscedastic linear regression model, obtaining some new estimators and interesting comparisons with existing estimators.
251 citations
TL;DR: In this paper, a local influence approach to the linear regression model with first-order autoregressive errors is developed and discussed, which avoids the inappropriate case-deletion diagnostic in the autoregression model and allows simultaneous perturbations on all responses.
35 citations
04 Apr 1992
34 citations
TL;DR: In this article, a stem profile model, fit using pseudo-likelihood weighted regression, was used to estimate merchantable volume of loblolly pine (Pinus taeda L.) in the southeast.
14 citations
Posted Content•
2 citations
TL;DR: In this paper, the authors describe how pedagogical benefits can be achieved in the comprehension of (frequently) difficult multiple regression concepts by following Martin Gardner's injunction to simplify the problem.
Abstract: This article describes how pedagogical benefits can be achieved in the comprehension of (frequently) difficult multiple regression concepts by following Martin Gardner's injunction to simplify the problem. Specifically presenting the simplest multiple regression model (two independent variables) with the smallest nondegenerate data set (four points) and systematically changing the arrangement of the points, graphically one gains intuition into many important multiple regression concepts. These include the following: the size and determination of s 2 = , the size and meaning of R 2, the significance of the overall regression model, the size and significance of each of the model's coefficients, multicolinearity, and how the location of the underlying data set influences each of these.
1 citations
01 Jan 1992
TL;DR: In this article, the uncertainty of the background, which determines to a large extent the minimal detectable signal and the calculated concentration, depend on the uncertainties of the slope and intercept of a linear relationship.
Abstract: To determine the background under an ionization edge, the pre-edge background intensities are extrapolated using a function which describes the intensity decrease as a function of the energy loss. When intensities and energy losses are logarithmically transformed, a linear relationship is found. The uncertainty of the background, which determines to a large extent the minimal detectable signal and the uncertainty of the calculated concentration, depend on the uncertainties of the slope and intercept of this linear relationship. The uncertainties in slope and intercept must be estimated by a weighted linear regression procedure if the variances of the intensities are non-uniform. If the variances of the normal distributed intensities are determined with few degrees of freedom, they are not suited as weight factors in the least squares minimalisation, however they can be replaced by smoothed values. These smoothed values are calculated with variance functions which describe the relation between the variance and the intensity. The results of the weighted least squares estimation with the smoothed variances did not differ much from the results of an un weighted regression. The weighted regression with the experimental variances led to erroneous results.