Huber approximation for the non-linear ℓ1 problem

Cataloged from PDF version of article.The smooth Huber approximation to the non-linear ‘1 problem was proposed by Tishler and Zang (1982), and further developed in Yang (1995). In the present paper, we use the ideas of Gould (1989) to give a new algorithm with rate of convergence results for the smooth Huber approximation. Results of computational tests are reported. 2005 Elsevier B.V. All rights reserved

Huber approximation for the non-linear ℓ1 problem

The smooth Huber approximation to the non-linear ℓ1 problem was proposed by Tishler and Zang (1982), and further developed in Yang (1995). In the present paper, we use the ideas of Gould (1989) to give a new algorithm with rate of convergence results for the smooth Huber approximation. Results of computational tests are reported. © 2005 Elsevier B.V. All rights reserved

Quantile Regression and Bass Models in Hydrology

Spatiotemporal phenomena related to the rainfall measurements can be characterised by statistical models grounded on physical concepts instead of being identified by spatiotemporal patterns based on standard correlations and related analytical tools. This perspective is useful in understanding if the relationships among neighbouring zones and consecutive years are attributable to latent physical mechanisms. Satellite data are used to examine this theory and provide evidence on empirical basis. A recent hydrological theory, which is based on the concept of self-organisation, consists of simplified physical mechanisms that are essential for the explanation of local data relationships. The regression models inspired by the diffusion of innovation can approximate the evolution of the rainfall process within a year through a more straightforward perspective. However, the multitude of collected data requires innovative techniques of data management and advanced analytical solutions, in order to achieve optimal results in reasonable time. Indeed, the nonlinear least squares and nonlinear quantile regression are considered to make inference on the response variable given some covariates. A new quantile regression technique is developed in order to provide simultaneous estimates that do not violate the monotonicity property of quantiles. The nonlinear least squares highlight strong connections among rainfall and the salient features of the measurements areas. Furthermore, the quantile regression analyses quantify the intrinsic variability of the data