Robust Inference Using the Exponential-Polynomial Divergence
Density-based minimum divergence procedures represent popular techniques in parametric statistical inference. They combine strong robustness properties with high (sometimes full) asymptotic efficiency. Among density-based minimum distance procedures, the methods based on the Brègman divergence have...
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| Vydáno v: | Journal of statistical theory and practice Ročník 15; číslo 2 |
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01.06.2021
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| Abstract | Density-based minimum divergence procedures represent popular techniques in parametric statistical inference. They combine strong robustness properties with high (sometimes full) asymptotic efficiency. Among density-based minimum distance procedures, the methods based on the Brègman divergence have the attractive property that the empirical formulation of the divergence does not require the use of any nonparametric smoothing technique such as kernel density estimation. The methods based on the density power divergence (DPD) represent the current standard in this area of research. In this paper, we will present a more generalized divergence which subsumes the DPD as a special case, and produces several new options providing better compromises between robustness and efficiency. |
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| AbstractList | Density-based minimum divergence procedures represent popular techniques in parametric statistical inference. They combine strong robustness properties with high (sometimes full) asymptotic efficiency. Among density-based minimum distance procedures, the methods based on the Brègman divergence have the attractive property that the empirical formulation of the divergence does not require the use of any nonparametric smoothing technique such as kernel density estimation. The methods based on the density power divergence (DPD) represent the current standard in this area of research. In this paper, we will present a more generalized divergence which subsumes the DPD as a special case, and produces several new options providing better compromises between robustness and efficiency. |
| ArticleNumber | 29 |
| Author | Singh, Pushpinder Basu, Ayanendranath Mandal, Abhijit |
| Author_xml | – sequence: 1 givenname: Pushpinder surname: Singh fullname: Singh, Pushpinder organization: Interdisciplinary Statistical Research Unit, Indian Statistical Institute – sequence: 2 givenname: Abhijit surname: Mandal fullname: Mandal, Abhijit organization: Department of Mathematical Sciences, University of Texas at El Paso – sequence: 3 givenname: Ayanendranath orcidid: 0000-0003-1416-9109 surname: Basu fullname: Basu, Ayanendranath email: ayanbasu@isical.ac.in organization: Interdisciplinary Statistical Research Unit, Indian Statistical Institute |
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| Keywords | Robustness Density power divergence Brègman divergence M-estimator |
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| References | JanaSBasuAA characterization of all single-integral, non-kernel divergence estimatorsIEEE Trans Inf Theory2019651279767984403891110.1109/TIT.2019.2937527 KullbackSLeiblerRAOn information and sufficiencyAnn Math Stat195122179863996810.1214/aoms/1177729694 MaronnaRAMartinRDYohaiVJSalibián-BarreraMRobust statistics: theory and methods (with R)2019New JerseyJohn Wiley and Sons1409.62009 Basak S, Basu A, Jones M (2020) On the ‘optimal’ density power divergence tuning parameter. J Appl Stat. (in press) BasuAShioyaHParkCStatistical inference: the minimum distance approach2011Boca RatonChapman and Hall10.1201/b10956 BasuAHarrisIRHjortNLJonesMRobust and efficient estimation by minimising a density power divergenceBiometrika1998853549559166587310.1093/biomet/85.3.549 WarwickJJonesMChoosing a robustness tuning parameterJ Stat Comput Simul2005757581588216254710.1080/00949650412331299120 MukherjeeTMandalABasuAThe B-exponential divergence and its generalizations with applications to parametric estimationStat Methods Appl2019282241257395440710.1007/s10260-018-00444-8 SimpsonDGHellinger deviance tests: efficiency, breakdown points, and examplesJ Am Stat Assoc19898440510711399966710.1080/01621459.1989.10478744 PardoLStatistical interference based on divergence measures2006Boca RatonChapman Hall/CRC1118.62008 StiglerSMDo robust estimators work with real data?Ann Stat1977561055109845520510.1214/aos/1176343997 BeranRMinimum hellinger distance estimates for parametric modelsAnn Stat1977534454634487000381.62028 GhoshABasuARobust estimation for independent non-homogeneous observations using density power divergence with applications to linear regressionElectron J Stat2013724202456311710210.1214/13-EJS847 LehmannELTheory of point estimation1983BerlinSpringer10.1007/978-1-4757-2769-2 SpiegelhalterDExact bayesian inference on the parameter of a cauchy distribution with vague prior informationBayesian Stat198527437498625170671.62026 HampelFRRonchettiEMRousseeuwPJStahelWARobust statistics: the approach based on influence functions2011New JerseyJohn Wiley and Sons0593.62027 RousseeuwPJLeroyAMRobust regression and outlier detection2005New JerseyJohn Wiley and Sons0711.62030 BrègmanLThe relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programmingComput Math Math Phys19677320021721561710.1016/0041-5553(67)90040-7 GhoshABasuARobust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approachJ Appl Stat201542920562072337104010.1080/02664763.2015.1016901 WelchWJRerandomizing the median in matched-pairs designsBiometrika198774360961490936510.1093/biomet/74.3.609 NelsonWGraphical analysis of accelerated life test data with the inverse power law modelIEEE Trans Reliab197221121110.1109/TR.1972.5216164 RA Maronna (162_CR12) 2019 A Ghosh (162_CR6) 2013; 7 EL Lehmann (162_CR11) 1983 W Nelson (162_CR14) 1972; 21 J Warwick (162_CR20) 2005; 75 D Spiegelhalter (162_CR18) 1985; 2 WJ Welch (162_CR21) 1987; 74 R Beran (162_CR4) 1977; 5 L Brègman (162_CR5) 1967; 7 A Ghosh (162_CR7) 2015; 42 162_CR1 S Kullback (162_CR10) 1951; 22 A Basu (162_CR2) 1998; 85 SM Stigler (162_CR19) 1977; 5 L Pardo (162_CR15) 2006 PJ Rousseeuw (162_CR16) 2005 DG Simpson (162_CR17) 1989; 84 A Basu (162_CR3) 2011 S Jana (162_CR9) 2019; 65 T Mukherjee (162_CR13) 2019; 28 FR Hampel (162_CR8) 2011 |
| References_xml | – reference: KullbackSLeiblerRAOn information and sufficiencyAnn Math Stat195122179863996810.1214/aoms/1177729694 – reference: MukherjeeTMandalABasuAThe B-exponential divergence and its generalizations with applications to parametric estimationStat Methods Appl2019282241257395440710.1007/s10260-018-00444-8 – reference: RousseeuwPJLeroyAMRobust regression and outlier detection2005New JerseyJohn Wiley and Sons0711.62030 – reference: SpiegelhalterDExact bayesian inference on the parameter of a cauchy distribution with vague prior informationBayesian Stat198527437498625170671.62026 – reference: WelchWJRerandomizing the median in matched-pairs designsBiometrika198774360961490936510.1093/biomet/74.3.609 – reference: JanaSBasuAA characterization of all single-integral, non-kernel divergence estimatorsIEEE Trans Inf Theory2019651279767984403891110.1109/TIT.2019.2937527 – reference: BrègmanLThe relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programmingComput Math Math Phys19677320021721561710.1016/0041-5553(67)90040-7 – reference: SimpsonDGHellinger deviance tests: efficiency, breakdown points, and examplesJ Am Stat Assoc19898440510711399966710.1080/01621459.1989.10478744 – reference: BasuAShioyaHParkCStatistical inference: the minimum distance approach2011Boca RatonChapman and Hall10.1201/b10956 – reference: HampelFRRonchettiEMRousseeuwPJStahelWARobust statistics: the approach based on influence functions2011New JerseyJohn Wiley and Sons0593.62027 – reference: BasuAHarrisIRHjortNLJonesMRobust and efficient estimation by minimising a density power divergenceBiometrika1998853549559166587310.1093/biomet/85.3.549 – reference: LehmannELTheory of point estimation1983BerlinSpringer10.1007/978-1-4757-2769-2 – reference: MaronnaRAMartinRDYohaiVJSalibián-BarreraMRobust statistics: theory and methods (with R)2019New JerseyJohn Wiley and Sons1409.62009 – reference: NelsonWGraphical analysis of accelerated life test data with the inverse power law modelIEEE Trans Reliab197221121110.1109/TR.1972.5216164 – reference: WarwickJJonesMChoosing a robustness tuning parameterJ Stat Comput Simul2005757581588216254710.1080/00949650412331299120 – reference: StiglerSMDo robust estimators work with real data?Ann Stat1977561055109845520510.1214/aos/1176343997 – reference: GhoshABasuARobust estimation for independent non-homogeneous observations using density power divergence with applications to linear regressionElectron J Stat2013724202456311710210.1214/13-EJS847 – reference: PardoLStatistical interference based on divergence measures2006Boca RatonChapman Hall/CRC1118.62008 – reference: Basak S, Basu A, Jones M (2020) On the ‘optimal’ density power divergence tuning parameter. J Appl Stat. (in press) – reference: BeranRMinimum hellinger distance estimates for parametric modelsAnn Stat1977534454634487000381.62028 – reference: GhoshABasuARobust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approachJ Appl Stat201542920562072337104010.1080/02664763.2015.1016901 – volume-title: Statistical inference: the minimum distance approach year: 2011 ident: 162_CR3 doi: 10.1201/b10956 – volume: 22 start-page: 79 issue: 1 year: 1951 ident: 162_CR10 publication-title: Ann Math Stat doi: 10.1214/aoms/1177729694 – volume-title: Theory of point estimation year: 1983 ident: 162_CR11 doi: 10.1007/978-1-4757-2769-2 – volume-title: Robust regression and outlier detection year: 2005 ident: 162_CR16 – volume: 28 start-page: 241 issue: 2 year: 2019 ident: 162_CR13 publication-title: Stat Methods Appl doi: 10.1007/s10260-018-00444-8 – volume: 85 start-page: 549 issue: 3 year: 1998 ident: 162_CR2 publication-title: Biometrika doi: 10.1093/biomet/85.3.549 – volume: 7 start-page: 200 issue: 3 year: 1967 ident: 162_CR5 publication-title: Comput Math Math Phys doi: 10.1016/0041-5553(67)90040-7 – ident: 162_CR1 doi: 10.1080/02664763.2020.1736524 – volume: 74 start-page: 609 issue: 3 year: 1987 ident: 162_CR21 publication-title: Biometrika doi: 10.1093/biomet/74.3.609 – volume: 5 start-page: 445 issue: 3 year: 1977 ident: 162_CR4 publication-title: Ann Stat – volume: 21 start-page: 2 issue: 1 year: 1972 ident: 162_CR14 publication-title: IEEE Trans Reliab doi: 10.1109/TR.1972.5216164 – volume: 65 start-page: 7976 issue: 12 year: 2019 ident: 162_CR9 publication-title: IEEE Trans Inf Theory doi: 10.1109/TIT.2019.2937527 – volume: 7 start-page: 2420 year: 2013 ident: 162_CR6 publication-title: Electron J Stat doi: 10.1214/13-EJS847 – volume-title: Statistical interference based on divergence measures year: 2006 ident: 162_CR15 – volume: 5 start-page: 1055 issue: 6 year: 1977 ident: 162_CR19 publication-title: Ann Stat doi: 10.1214/aos/1176343997 – volume: 84 start-page: 107 issue: 405 year: 1989 ident: 162_CR17 publication-title: J Am Stat Assoc doi: 10.1080/01621459.1989.10478744 – volume: 2 start-page: 743 year: 1985 ident: 162_CR18 publication-title: Bayesian Stat – volume: 42 start-page: 2056 issue: 9 year: 2015 ident: 162_CR7 publication-title: J Appl Stat doi: 10.1080/02664763.2015.1016901 – volume-title: Robust statistics: theory and methods (with R) year: 2019 ident: 162_CR12 – volume-title: Robust statistics: the approach based on influence functions year: 2011 ident: 162_CR8 – volume: 75 start-page: 581 issue: 7 year: 2005 ident: 162_CR20 publication-title: J Stat Comput Simul doi: 10.1080/00949650412331299120 |
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| Title | Robust Inference Using the Exponential-Polynomial Divergence |
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