Topic
Robust regression
About: Robust regression is a research topic. Over the lifetime, 2911 publications have been published within this topic receiving 169965 citations.
Papers published on a yearly basis
1 / 2
Papers
Book•
1 Jan 1966
TL;DR: In this article, the Straight Line Case is used to fit a straight line by least squares, and the Durbin-Watson Test is used for checking the straight line fit.
Abstract: Basic Prerequisite Knowledge. Fitting a Straight Line by Least Squares. Checking the Straight Line Fit. Fitting Straight Lines: Special Topics. Regression in Matrix Terms: Straight Line Case. The General Regression Situation. Extra Sums of Squares and Tests for Several Parameters Being Zero. Serial Correlation in the Residuals and the Durbin--Watson Test. More of Checking Fitted Models. Multiple Regression: Special Topics. Bias in Regression Estimates, and Expected Values of Mean Squares and Sums of Squares. On Worthwhile Regressions, Big F's, and R 2 . Models Containing Functions of the Predictors, Including Polynomial Models. Transformation of the Response Variable. "Dummy" Variables. Selecting the "Best" Regression Equation. Ill--Conditioning in Regression Data. Ridge Regression. Generalized Linear Models (GLIM). Mixture Ingredients as Predictor Variables. The Geometry of Least Squares. More Geometry of Least Squares. Orthogonal Polynomials and Summary Data. Multiple Regression Applied to Analysis of Variance Problems. An Introduction to Nonlinear Estimation. Robust Regression. Resampling Procedures (Bootstrapping). Bibliography. True/False Questions. Answers to Exercises. Tables. Indexes.
19,032 citations
TL;DR: Robust locally weighted regression as discussed by the authors is a method for smoothing a scatterplot, in which the fitted value at z k is the value of a polynomial fit to the data using weighted least squares, where the weight for (x i, y i ) is large if x i is close to x k and small if it is not.
Abstract: The visual information on a scatterplot can be greatly enhanced, with little additional cost, by computing and plotting smoothed points. Robust locally weighted regression is a method for smoothing a scatterplot, (x i , y i ), i = 1, …, n, in which the fitted value at z k is the value of a polynomial fit to the data using weighted least squares, where the weight for (x i , y i ) is large if x i is close to x k and small if it is not. A robust fitting procedure is used that guards against deviant points distorting the smoothed points. Visual, computational, and statistical issues of robust locally weighted regression are discussed. Several examples, including data on lead intoxication, are used to illustrate the methodology.
11,384 citations
TL;DR: In this paper, a method of estimating the parameters of a set of regression equations is reported which involves application of Aitken's generalized least-squares to the whole system of equations.
Abstract: In this paper a method of estimating the parameters of a set of regression equations is reported which involves application of Aitken's generalized least-squares [1] to the whole system of equations. Under conditions generally encountered in practice, it is found that the regression coefficient estimators so obtained are at least asymptotically more efficient than those obtained by an equation-by-equation application of least squares. This gain in efficiency can be quite large if “independent” variables in different equations are not highly correlated and if disturbance terms in different equations are highly correlated. Further, tests of the hypothesis that all regression equation coefficient vectors are equal, based on “micro” and “macro” data, are described. If this hypothesis is accepted, there will be no aggregation bias. Finally, the estimation procedure and the “micro-test” for aggregation bias are applied in the analysis of annual investment data, 1935–1954, for two firms.
8,362 citations
Book•
1 Jan 1987
TL;DR: This paper presents the results of a two-year study of the statistical treatment of outliers in the context of one-Dimensional Location and its applications to discrete-time reinforcement learning.
Abstract: 1. Introduction. 2. Simple Regression. 3. Multiple Regression. 4. The Special Case of One-Dimensional Location. 5. Algorithms. 6. Outlier Diagnostics. 7. Related Statistical Techniques. References. Table of Data Sets. Index.
7,051 citations
TL;DR: In this article, a new approach toward a theory of robust estimation is presented, which treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators that are asyptotically most robust (in a sense to be specified) among all translation invariant estimators.
Abstract: This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators—intermediaries between sample mean and sample median—that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators. For the general background, see Tukey (1960) (p. 448 ff.)
6,568 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 25 |
| 2024 | 50 |
| 2023 | 69 |
| 2022 | 131 |
| 2021 | 119 |
| 2020 | 120 |