Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis

Riani, Marco; Atkinson, Anthony C.; Corbellini, Aldo; Perrotta, Domenico

doi:10.3390/e22040399

Cited by 13 publications

(9 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, in some cases, it may be better to select an appropriate tuning parameter from among the γ candidates than to fix the value. The monitoring approach (Riani et al 2020) and robust cross-validation (Kawashima and Fujisawa 2017) can be utilized as a method of selecting γ .…”

Section: Discussionmentioning

confidence: 99%

“…Recently, some robust regression methods have been proposed based on divergences, using L 2 -divergence (Chi and Scott 2014;Lozano et al 2016), density power divergence (Ghosh and Basu 2016;Riani et al 2020;Ghosh and Majumdar 2020), and γ -divergence (Kawashima and Fujisawa 2017;Hung et al 2018;Ren et al 2020). In these methods, the robust properties are generally investigated under the contaminated model.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust regression against heavy heterogeneous contamination

Kawashima

Fujisawa

2022

Metrika

View full text Add to dashboard Cite

The $$\gamma $$ γ -divergence is well-known for having strong robustness against heavy contamination. By virtue of this property, many applications via the $$\gamma $$ γ -divergence have been proposed. There are two types of $$\gamma $$ γ -divergence for the regression problem, in which the base measures are handled differently. In this study, these two $$\gamma $$ γ -divergences are compared, and a large difference is found between them under heterogeneous contamination, where the outlier ratio depends on the explanatory variable. One $$\gamma $$ γ -divergence has the strong robustness even under heterogeneous contamination. The other does not have in general; however, it has under homogeneous contamination, where the outlier ratio does not depend on the explanatory variable, or when the parametric model of the response variable belongs to a location-scale family in which the scale does not depend on the explanatory variables. Hung et al. (Biometrics 74(1):145–154, 2018) discussed the strong robustness in a logistic regression model with an additional assumption that the tuning parameter $$\gamma $$ γ is sufficiently large. The results obtained in this study hold for any parametric model without such an additional assumption.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust regression against heavy heterogeneous contamination

Kawashima

Fujisawa

2022

Metrika

View full text Add to dashboard Cite

show abstract

“…The calculations to find c for given efficiency are given in their Section 3.2. Riani et al [29] shows plots exhibiting the relationship between bdp and efficiency for five ρ functions. A much fuller discussion of monitoring robust regression is [4], including examples of S, MM, LMS and LTS analyses using the FSDA.…”

Section: Monitoring and Graphicsmentioning

confidence: 99%

fsdaSAS: A Package for Robust Regression for Very Large Datasets Including the Batch Forward Search

Torti

Corbellini

Atkinson

2021

Stats

Self Cite

View full text Add to dashboard Cite

The forward search (FS) is a general method of robust data fitting that moves smoothly from very robust to maximum likelihood estimation. The regression procedures are included in the MATLAB toolbox FSDA. The work on a SAS version of the FS originates from the need for the analysis of large datasets expressed by law enforcement services operating in the European Union that use our SAS software for detecting data anomalies that may point to fraudulent customs returns. Specific to our SAS implementation, the fsdaSAS package, we describe the approximation used to provide fast analyses of large datasets using an FS which progresses through the inclusion of batches of observations, rather than progressing one observation at a time. We do, however, test for outliers one observation at a time. We demonstrate that our SAS implementation becomes appreciably faster than the MATLAB version as the sample size increases and is also able to analyse larger datasets. The series of fits provided by the FS leads to the adaptive data-dependent choice of maximally efficient robust estimates. This also allows the monitoring of residuals and parameter estimates for fits of differing robustness levels. We mention that our fsdaSAS also applies the idea of monitoring to several robust estimators for regression for a range of values of breakdown point or nominal efficiency, leading to adaptive values for these parameters. We have also provided a variety of plots linked through brushing. Further programmed analyses include the robust transformations of the response in regression. Our package also provides the SAS community with methods of monitoring robust estimators for multivariate data, including multivariate data transformations.

show abstract

“…In this work, taking the approach of Gombay and Serban [30] and Huh, Kim and Lee [31], we designate a robust monitoring process based on the minimum distance power divergence estimator (MDPDE) proposed by Basu, Harris, Hjort and Jones [33]. We do this because the MDPDE is well-known to be suitable for robust inference in various models, having a trade-off between efficiency and robustness controlled through the tuning parameters with little loss in asymptotic efficiency relative to the maximum likelihood estimator (MLE) (Riani, Atkinson, Corbellini and Perrotta [34]). The MDPDE method has been successfully applied to various time series models, and in particular INGARCH models (Kim and Lee [35], Kim and Lee [36]).…”

Section: Introductionmentioning

confidence: 99%

Monitoring Parameter Change for Time Series Models of Counts Based on Minimum Density Power Divergence Estimator

Lee

Kim

2020

Entropy

View full text Add to dashboard Cite

In this study, we consider an online monitoring procedure to detect a parameter change for integer-valued generalized autoregressive heteroscedastic (INGARCH) models whose conditional density of present observations over past information follows one parameter exponential family distributions. For this purpose, we use the cumulative sum (CUSUM) of score functions deduced from the objective functions, constructed for the minimum power divergence estimator (MDPDE) that includes the maximum likelihood estimator (MLE), to diminish the influence of outliers. It is well-known that compared to the MLE, the MDPDE is robust against outliers with little loss of efficiency. This robustness property is properly inherited by the proposed monitoring procedure. A simulation study and real data analysis are conducted to affirm the validity of our method.

show abstract

Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis

Cited by 13 publications

References 27 publications

Robust regression against heavy heterogeneous contamination

Robust regression against heavy heterogeneous contamination

fsdaSAS: A Package for Robust Regression for Very Large Datasets Including the Batch Forward Search

Monitoring Parameter Change for Time Series Models of Counts Based on Minimum Density Power Divergence Estimator

Contact Info

Product

Resources

About