Showing papers by "Ingram Olkin published in 1992"
TL;DR: Gini regression as discussed by the authors is equivalent to OLS when the assumptions hold, and is more robust when the assumption fails, and Gini regression can also be used to test the validity of the assumptions.
Abstract: The method of least squares ranks as one of the most commonly used methods for estimating the relation between a set of variables on the conditional expected value of another variable. Ordinary Least Squares (OLS) relies on several assumptions, which when violated may not yield robust estimates. In this paper we pose alternative ways to view this model. In particular we study Gini regression which is equivalent to OLS when the assumptions hold, and is more robust when the assumptions fail. Gini regression can also be used to test the validity of the assumptions.
101 citations
TL;DR: There have been many studies on the detection of outliers as discussed by the authors, and it has been shown that the deviation of any particular observation from the mean is bounded by a multiple of the standard deviation.
Abstract: There have been many studies on the detection of outliers. In one of the very early articles it was shown that the deviation of any particular observation from the mean is bounded by a multiple of the standard deviation. This result is simple and has resulted in periodic rediscoveries, coupled with a variety of alternative proofs. We provide a historical review of these various methods, and then pose yet another proof that may have some intrinsic interest.
20 citations
TL;DR: In this article, the authors present some simulation procedures that address the difficulties of robustness analysis when distributional assumptions are not met and when the analysis of contaminated data involves substantial computational problems, which is a common problem in robustness analyses.
Abstract: Mixtures of normal distributions arise naturally in robustness analyses when distributional assumptions are not met and with the analysis of contaminated data. Typically these analyses involve substantial computational problems. We present some simulation procedures that address these difficulties.
9 citations
7 citations