Least squares is probably the best known method for fitting linear models and by far the most widely used. Surprisingly, the discrete L 1 analogue, least absolute deviations (LAD) seems to have been considered first. Possibly the LAD criterion was forced into the background because of the com­ putational difficulties associated with it. Recently there has been a resurgence of interest in LAD. It was spurred on by work that has resulted in efficient al­ gorithms for obtaining LAD fits. Another stimulus came from robust statistics. LAD estimates resist undue effects from a feyv, large errors. Therefore. in addition to being robust, they also make good starting points for other iterative, robust procedures. The LAD criterion has great utility. LAD fits are optimal for linear regressions where the errors are double exponential. However they also have excellent properties well outside this narrow context. In addition they are useful in other linear situations such as time series and multivariate data analysis. Finally, LAD fitting embodies a set of ideas that is important in linear optimization theory and numerical analysis. viii PREFACE In this monograph we will present a unified treatment of the role of LAD techniques in several domains. Some of the material has appeared in recent journal papers and some of it is new. This presentation is organized in the following way. There are three parts, one for Theory, one for Applicatior.s and one for Algorithms.

Least squares is probably the best known method for fitting linear models and by far the most widely used. Surprisingly, the discrete L 1 analogue, least absolute deviations (LAD) seems to have been considered first. Possibly the LAD criterion was forced into the background because of the com­ putational difficulties associated with it. Recently there has been a resurgence of interest in LAD. It was spurred on by work that has resulted in efficient al­ gorithms for obtaining LAD fits. Another stimulus came from robust statistics. LAD estimates resist undue effects from a feyv, large errors. Therefore. in addition to being robust, they also make good starting points for other iterative, robust procedures. The LAD criterion has great utility. LAD fits are optimal for linear regressions where the errors are double exponential. However they also have excellent properties well outside this narrow context. In addition they are useful in other linear situations such as time series and multivariate data analysis. Finally, LAD fitting embodies a set of ideas that is important in linear optimization theory and numerical analysis. viii PREFACE In this monograph we will present a unified treatment of the role of LAD techniques in several domains. Some of the material has appeared in recent journal papers and some of it is new. This presentation is organized in the following way. There are three parts, one for Theory, one for Applicatior.s and one for Algorithms.

This volume contains the proceedings of the workshop on "Soil Monitoring: Methods for Early Detection and Surveying of Soil Contamination and Degradation", held at the ETH seminar centre "Stefano Franscini" of Monte Verita, Ascona (Switzerland) from October 18 - 23, 1992. Seventy participants, representing a variety of institutions, nations, and disciplines, discussed the concepts, approaches, status, gaps, problems, and perspectives of soil pollution monitoring. The idea for this workshop came from A. Desaules when he was installing the Swiss National Soil Monitoring Network (NABO) as his doubts about the philosophy of soil monitoring prevailing at that time increased. This philosophy essentially equated soil mo­ nitoring with repetitive surveys of soil pollutant concentrations at pennanent observation sites. He sought others interested in discussing alternatives, and he found a ready partner in the ETH-Institute for Terrestrial Ecology. Soon it was realized that a discussion of the NABO would immediately raise general questions with respect to the conceptual basis of soil monitoring and that a minimum agreement on this basis was indispensable to discuss more specific problems related to the realization of the NABO. As a result, a workshop was organized whose objectives were in particular (i) an assessment of current knowledge on soil monitoring by pennanent networks, (ii) a syn­ thesis of the experience from different disciplines related to soil monitoring, (iii) the identification ofresearch gaps with respect to long-tenn and large-scale soil monitoring, and (iv) the design of a platfonn for the development of soil monitoring strategies and methodology.

Least squares is probably the best known method for fitting linear models and by far the most widely used. Surprisingly, the discrete L 1 analogue, least absolute deviations (LAD) seems to have been considered first. Possibly the LAD criterion was forced into the background because of the com­ putational difficulties associated with it. Recently there has been a resurgence of interest in LAD. It was spurred on by work that has resulted in efficient al­ gorithms for obtaining LAD fits. Another stimulus came from robust statistics. LAD estimates resist undue effects from a feyv, large errors. Therefore. in addition to being robust, they also make good starting points for other iterative, robust procedures. The LAD criterion has great utility. LAD fits are optimal for linear regressions where the errors are double exponential. However they also have excellent properties well outside this narrow context. In addition they are useful in other linear situations such as time series and multivariate data analysis. Finally, LAD fitting embodies a set of ideas that is important in linear optimization theory and numerical analysis. viii PREFACE In this monograph we will present a unified treatment of the role of LAD techniques in several domains. Some of the material has appeared in recent journal papers and some of it is new. This presentation is organized in the following way. There are three parts, one for Theory, one for Applicatior.s and one for Algorithms.

Least squares is probably the best known method for fitting linear models and by far the most widely used. Surprisingly, the discrete L 1 analogue, least absolute deviations (LAD) seems to have been considered first. Possibly the LAD criterion was forced into the background because of the com­ putational difficulties associated with it. Recently there has been a resurgence of interest in LAD. It was spurred on by work that has resulted in efficient al­ gorithms for obtaining LAD fits. Another stimulus came from robust statistics. LAD estimates resist undue effects from a feyv, large errors. Therefore. in addition to being robust, they also make good starting points for other iterative, robust procedures. The LAD criterion has great utility. LAD fits are optimal for linear regressions where the errors are double exponential. However they also have excellent properties well outside this narrow context. In addition they are useful in other linear situations such as time series and multivariate data analysis. Finally, LAD fitting embodies a set of ideas that is important in linear optimization theory and numerical analysis. viii PREFACE In this monograph we will present a unified treatment of the role of LAD techniques in several domains. Some of the material has appeared in recent journal papers and some of it is new. This presentation is organized in the following way. There are three parts, one for Theory, one for Applicatior.s and one for Algorithms.

This volume contains the proceedings of the workshop on "Soil Monitoring: Methods for Early Detection and Surveying of Soil Contamination and Degradation", held at the ETH seminar centre "Stefano Franscini" of Monte Verita, Ascona (Switzerland) from October 18 - 23, 1992. Seventy participants, representing a variety of institutions, nations, and disciplines, discussed the concepts, approaches, status, gaps, problems, and perspectives of soil pollution monitoring. The idea for this workshop came from A. Desaules when he was installing the Swiss National Soil Monitoring Network (NABO) as his doubts about the philosophy of soil monitoring prevailing at that time increased. This philosophy essentially equated soil mo­ nitoring with repetitive surveys of soil pollutant concentrations at pennanent observation sites. He sought others interested in discussing alternatives, and he found a ready partner in the ETH-Institute for Terrestrial Ecology. Soon it was realized that a discussion of the NABO would immediately raise general questions with respect to the conceptual basis of soil monitoring and that a minimum agreement on this basis was indispensable to discuss more specific problems related to the realization of the NABO. As a result, a workshop was organized whose objectives were in particular (i) an assessment of current knowledge on soil monitoring by pennanent networks, (ii) a syn­ thesis of the experience from different disciplines related to soil monitoring, (iii) the identification ofresearch gaps with respect to long-tenn and large-scale soil monitoring, and (iv) the design of a platfonn for the development of soil monitoring strategies and methodology.