Least Absolute Deviations: Theory, Applications and Algorithms
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1983
|
| Schriftenreihe: | Progress in Probability and Statistics
6 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XIV, 351 p) |
| ISBN: | 9781468485745 |
| DOI: | 10.1007/978-1-4684-8574-5 |
Internformat
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| 500 | |a 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 | ||
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Datensatz im Suchindex
| _version_ | 1804153093882904576 |
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| any_adam_object | |
| author | Bloomfield, Peter 1946- Steiger, William L. |
| author_GND | (DE-588)143534424 (DE-588)170541134 |
| author_facet | Bloomfield, Peter 1946- Steiger, William L. |
| author_role | aut aut |
| author_sort | Bloomfield, Peter 1946- |
| author_variant | p b pb w l s wl wls |
| building | Verbundindex |
| bvnumber | BV042421150 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-8574-5 |
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| id | DE-604.BV042421150 |
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| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468485745 |
| language | English |
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| spelling | Bloomfield, Peter 1946- Verfasser (DE-588)143534424 aut Least Absolute Deviations Theory, Applications and Algorithms by Peter Bloomfield, William L. Steiger Boston, MA Birkhäuser Boston 1983 1 Online-Ressource (XIV, 351 p) txt rdacontent c rdamedia cr rdacarrier Progress in Probability and Statistics 6 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 Mathematics Algorithms Distribution (Probability theory) Probability Theory and Stochastic Processes Applications of Mathematics Mathematik Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Kleinste absolute Abweichung (DE-588)4501130-8 gnd rswk-swf Ausgleichsrechnung (DE-588)4143526-6 gnd rswk-swf Kleinste absolute Abweichung (DE-588)4501130-8 s Regressionsanalyse (DE-588)4129903-6 s 1\p DE-604 Ausgleichsrechnung (DE-588)4143526-6 s 2\p DE-604 Steiger, William L. Verfasser (DE-588)170541134 aut Erscheint auch als Druck-Ausgabe 978-1-4684-8576-9 https://doi.org/10.1007/978-1-4684-8574-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bloomfield, Peter 1946- Steiger, William L. Least Absolute Deviations Theory, Applications and Algorithms Mathematics Algorithms Distribution (Probability theory) Probability Theory and Stochastic Processes Applications of Mathematics Mathematik Regressionsanalyse (DE-588)4129903-6 gnd Kleinste absolute Abweichung (DE-588)4501130-8 gnd Ausgleichsrechnung (DE-588)4143526-6 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4501130-8 (DE-588)4143526-6 |
| title | Least Absolute Deviations Theory, Applications and Algorithms |
| title_auth | Least Absolute Deviations Theory, Applications and Algorithms |
| title_exact_search | Least Absolute Deviations Theory, Applications and Algorithms |
| title_full | Least Absolute Deviations Theory, Applications and Algorithms by Peter Bloomfield, William L. Steiger |
| title_fullStr | Least Absolute Deviations Theory, Applications and Algorithms by Peter Bloomfield, William L. Steiger |
| title_full_unstemmed | Least Absolute Deviations Theory, Applications and Algorithms by Peter Bloomfield, William L. Steiger |
| title_short | Least Absolute Deviations |
| title_sort | least absolute deviations theory applications and algorithms |
| title_sub | Theory, Applications and Algorithms |
| topic | Mathematics Algorithms Distribution (Probability theory) Probability Theory and Stochastic Processes Applications of Mathematics Mathematik Regressionsanalyse (DE-588)4129903-6 gnd Kleinste absolute Abweichung (DE-588)4501130-8 gnd Ausgleichsrechnung (DE-588)4143526-6 gnd |
| topic_facet | Mathematics Algorithms Distribution (Probability theory) Probability Theory and Stochastic Processes Applications of Mathematics Mathematik Regressionsanalyse Kleinste absolute Abweichung Ausgleichsrechnung |
| url | https://doi.org/10.1007/978-1-4684-8574-5 |
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