Alternative ridge robust regression estimator for dealing with collinear influential data points

2015 ◽  
Vol 10 ◽  
pp. 119-130
Author(s):  
Moawad El-Fallah Abd El-Salam
Keyword(s):  
Robust Regression ◽  
Regression Estimator ◽  
Data Points

Influential Observations and Inference in Accounting Research

2016 ◽  
Vol 94 (6) ◽  
pp. 337-364 ◽  
Author(s):  
Andrew J. Leone ◽  
Miguel Minutti-Meza ◽  
Charles E. Wasley
Keyword(s):  
Robust Regression ◽  
Extreme Values ◽  
Data Availability ◽  
Influence Coefficient ◽  
Influential Observations ◽  
Coefficient Estimates ◽  
The Public ◽  
Influence Diagnostics ◽  
Sensitivity Tests ◽  
Data Points

ABSTRACT Accounting studies often encounter observations with extreme values that can influence coefficient estimates and inferences. Two widely used approaches to address influential observations in accounting studies are winsorization and truncation. While expedient, both depend on researcher-selected cutoffs, applied on a variable-by-variable basis, which, unfortunately, can alter legitimate data points. We compare the efficacy of winsorization, truncation, influence diagnostics (Cook's Distance), and robust regression at identifying influential observations. Replication of three published accounting studies shows that the choice impacts estimates and inferences. Simulation evidence shows that winsorization and truncation are ineffective at identifying influential observations. While influence diagnostics and robust regression both outperform winsorization and truncation, overall, robust regression outperforms the other methods. Since robust regression is a theoretically appealing and easily implementable approach based on a model's residuals, we recommend that future accounting studies consider using robust regression, or at least report sensitivity tests using robust regression. JEL Classifications: C12; C13; C18; C51; C52; M41. Data Availability: Data are available from the public sources cited in the text.

scholarly journals Leveraged least trimmed absolute deviations

OR Spectrum ◽  
2021 ◽  
Author(s):  
Nathan Sudermann-Merx ◽  
Steffen Rebennack
Keyword(s):  
Regression Models ◽  
Robust Regression ◽  
Mixed Integer ◽  
Benchmark Problems ◽  
Data Sets ◽  
Least Trimmed Squares ◽  
Binary Variables ◽  
Leverage Point ◽  
Data Points ◽  
Numerical Complexity

AbstractThe design of regression models that are not affected by outliers is an important task which has been subject of numerous papers within the statistics community for the last decades. Prominent examples of robust regression models are least trimmed squares (LTS), where the k largest squared deviations are ignored, and least trimmed absolute deviations (LTA) which ignores the k largest absolute deviations. The numerical complexity of both models is driven by the number of binary variables and by the value k of ignored deviations. We introduce leveraged least trimmed absolute deviations (LLTA) which exploits that LTA is already immune against y-outliers. Therefore, LLTA has only to be guarded against outlying values in x, so-called leverage points, which can be computed beforehand, in contrast to y-outliers. Thus, while the mixed-integer formulations of LTS and LTA have as many binary variables as data points, LLTA only needs one binary variable per leverage point, resulting in a significant reduction of binary variables. Based on 11 data sets from the literature, we demonstrate that (1) LLTA’s prediction quality improves much faster than LTS and as fast as LTA for increasing values of k and (2) that LLTA solves the benchmark problems about 80 times faster than LTS and about five times faster than LTA, in median.

scholarly journals Consistency of Penalized Convex Regression

2020 ◽  
Vol 10 (1) ◽  
pp. 69
Author(s):  
Eunji Lim
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Simple Approach ◽  
Regression Estimator ◽  
Data Points ◽  
Convex Regression

We consider the problem of estimating an unknown convex function f_* (0, 1)^d →R from data (X1, Y1), … (X_n; Y_n).A simple approach is finding a convex function that is the closest to the data points by minimizing the sum of squared errors over all convex functions. The convex regression estimator, which is computed this way, su ers from a drawback of having extremely large subgradients near the boundary of its domain. To remedy this situation, the penalized convex regression estimator, which minimizes the sum of squared errors plus the sum of squared norms of the subgradient over all convex functions, is recently proposed. In this paper, we prove that the penalized convex regression estimator and its subgradient converge with probability one to f_* and its subgradient, respectively, as n → ∞, and hence, establish the legitimacy of the penalized convex regression estimator.  

point-Analysis Using the Extrapolation Method in the Analytical Electron microscope

1990 ◽  
Vol 48 (2) ◽  
pp. 430-431
Author(s):  
Zenji Horita ◽  
Ryuzo Nishimachi ◽  
Takeshi Sano ◽  
Minoru Nemoto
Keyword(s):  
Electron Microscope ◽  
Extrapolation Method ◽  
X Ray ◽  
Absorption Correction ◽  
Point Analysis ◽  
Analytical Electron ◽  
Analytical Electron Microscope ◽  
Data Points ◽  
Identical Composition ◽  
X Ray Absorption

Absorption correction is often required in quantitative x-ray microanalysis of thin specimens using the analytical electron microscope. For such correction, it is convenient to use the extrapolation method[l] because the thickness, density and mass absorption coefficient are not necessary in the method. The characteristic x-ray intensities measured for the analysis are only requirement for the absorption correction. However, to achieve extrapolation, it is imperative to obtain data points more than two at different thicknesses in the identical composition. Thus, the method encounters difficulty in analyzing a region equivalent to beam size or the specimen with uniform thickness. The purpose of this study is to modify the method so that extrapolation becomes feasible in such limited conditions. Applicability of the new form is examined by using a standard sample and then it is applied to quantification of phases in a Ni-Al-W ternary alloy.The earlier equation for the extrapolation method was formulated based on the facts that the magnitude of x-ray absorption increases with increasing thickness and that the intensity of a characteristic x-ray exhibiting negligible absorption in the specimen is used as a measure of thickness.

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