scholarly journals Robust estimation for independent non-homogeneous observations using density power divergence with applications to linear regression

2013 ◽  
Vol 7 (0) ◽  
pp. 2420-2456 ◽  
Author(s):  
Abhik Ghosh ◽  
Ayanendranath Basu
Keyword(s):  
Linear Regression ◽  
Robust Estimation ◽  
Density Power Divergence ◽  
Power Divergence

scholarly journals Robust Estimation for Bivariate Poisson INGARCH Models

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 367
Author(s):  
Byungsoo Kim ◽  
Sangyeol Lee ◽  
Dongwon Kim
Keyword(s):  
Robust Estimation ◽  
New South ◽  
Estimation Method ◽  
Real Data ◽  
Regularity Conditions ◽  
Density Power Divergence ◽  
Asymptotically Normal ◽  
South Wales ◽  
Power Divergence ◽  
Conditional Maximum

In the integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, parameter estimation is conventionally based on the conditional maximum likelihood estimator (CMLE). However, because the CMLE is sensitive to outliers, we consider a robust estimation method for bivariate Poisson INGARCH models while using the minimum density power divergence estimator. We demonstrate the proposed estimator is consistent and asymptotically normal under certain regularity conditions. Monte Carlo simulations are conducted to evaluate the performance of the estimator in the presence of outliers. Finally, a real data analysis using monthly count series of crimes in New South Wales and an artificial data example are provided as an illustration.

scholarly journals On Selection Criteria for the Tuning Parameter in Robust Divergence

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1147
Author(s):  
Shonosuke Sugasawa ◽  
Shouto Yonekura
Keyword(s):  
Linear Regression ◽  
Asymptotic Approximation ◽  
Selection Criteria ◽  
Selection Criterion ◽  
Tuning Parameter ◽  
Density Power Divergence ◽  
Normal Distributions ◽  
Numerical Studies ◽  
Power Divergence ◽  
Derivatives Of

Although robust divergence, such as density power divergence and γ-divergence, is helpful for robust statistical inference in the presence of outliers, the tuning parameter that controls the degree of robustness is chosen in a rule-of-thumb, which may lead to an inefficient inference. We here propose a selection criterion based on an asymptotic approximation of the Hyvarinen score applied to an unnormalized model defined by robust divergence. The proposed selection criterion only requires first and second-order partial derivatives of an assumed density function with respect to observations, which can be easily computed regardless of the number of parameters. We demonstrate the usefulness of the proposed method via numerical studies using normal distributions and regularized linear regression.

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

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 399 ◽  
Author(s):  
Marco Riani ◽  
Anthony C. Atkinson ◽  
Aldo Corbellini ◽  
Domenico Perrotta
Keyword(s):  
Robust Regression ◽  
Robust Statistics ◽  
Estimation Method ◽  
Estimation Procedure ◽  
Breakdown Point ◽  
Parameter Estimates ◽  
Normal Density ◽  
Density Power Divergence ◽  
Numerical Minimization ◽  
Power Divergence

Minimum density power divergence estimation provides a general framework for robust statistics, depending on a parameter α , which determines the robustness properties of the method. The usual estimation method is numerical minimization of the power divergence. The paper considers the special case of linear regression. We developed an alternative estimation procedure using the methods of S-estimation. The rho function so obtained is proportional to one minus a suitably scaled normal density raised to the power α . We used the theory of S-estimation to determine the asymptotic efficiency and breakdown point for this new form of S-estimation. Two sets of comparisons were made. In one, S power divergence is compared with other S-estimators using four distinct rho functions. Plots of efficiency against breakdown point show that the properties of S power divergence are close to those of Tukey’s biweight. The second set of comparisons is between S power divergence estimation and numerical minimization. Monitoring these two procedures in terms of breakdown point shows that the numerical minimization yields a procedure with larger robust residuals and a lower empirical breakdown point, thus providing an estimate of α leading to more efficient parameter estimates.

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