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Titlebook: Least Absolute Deviations; Theory, Applications Peter Bloomfield,William L. Steiger Book 1983 Springer Science+Business Media New York 1983

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书目名称Least Absolute Deviations
副标题Theory, Applications
编辑Peter Bloomfield,William L. Steiger
视频video
丛书名称Progress in Probability
图书封面Titlebook: Least Absolute Deviations; Theory, Applications Peter Bloomfield,William L. Steiger Book 1983 Springer Science+Business Media New York 1983
描述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 treat
出版日期Book 1983
关键词algorithms; linear optimization; numerical analysis; optimization; statistics
版次1
doihttps://doi.org/10.1007/978-1-4684-8574-5
isbn_softcover978-1-4684-8576-9
isbn_ebook978-1-4684-8574-5Series ISSN 1050-6977 Series E-ISSN 2297-0428
issn_series 1050-6977
copyrightSpringer Science+Business Media New York 1983
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发表于 2025-3-21 21:51:15 | 显示全部楼层
LAD in Linear Regression,Let . = (.,Y) ∈ R. be a random vector whose components obey the linear model . where . ∈ R. and the random variable U, E(U) = m, . given. If . and ∪ . independent E(U|.) = E(U) almost surely, and
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LAD in Multi-Way Tables,An important special case of the general linear model discussed in Chapters 1 and 2 is when the data fall into a multi-way table. The simplest case is the one-way layout, where the data . organized into c cells, with observations y., 1 ≤ k ≤ n., in the jth cell, 1 ≤ j ≤ c.
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Appendix,In this section we present the detailed results of the Monte-Carlo study described in Section 2.4. Samples of size n were generated from . where the n values of X. were ..
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https://doi.org/10.1007/978-1-4684-8574-5algorithms; linear optimization; numerical analysis; optimization; statistics
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