Resistant estimators in poisson and gamma models with missing responses and an application to outlier detection
When dealing with situations in which the responses are discrete or show some type of asymmetry, the linear model is not appropriate to establish the relation between the responses and the covariates. Generalized linear models serve this purpose, since they allow one to model the mean of the respons...
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paper:paper_0047259X_v114_n1_p209_Bianco2023-06-08T15:05:35Z Resistant estimators in poisson and gamma models with missing responses and an application to outlier detection Bianco, Ana María Boente, Graciela Lina Fisher-consistency Generalized linear models Missing data Outliers Robust estimation When dealing with situations in which the responses are discrete or show some type of asymmetry, the linear model is not appropriate to establish the relation between the responses and the covariates. Generalized linear models serve this purpose, since they allow one to model the mean of the responses through a link function, linearly on the covariates. When atypical observations are present in the sample, robust estimators are useful to provide fair estimations as well as to build outlier detection rules. The focus of this paper is to define robust estimators for the regression parameter when missing data possibly occur in the responses. The estimators introduced turn out to be consistent under mild conditions. In particular, resistant methods for Poisson and Gamma models are given. A simulation study allows one to compare the behaviour of the classical and robust estimators, under different contamination schemes. The robustness of the proposed procedures is studied through the influence function, while asymptotic variances are derived from it. Besides, outlier detection rules are defined using the influence function. The procedure is also illustrated by analysing a real data set. © 2012 Elsevier Inc. Fil:Bianco, A.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Boente, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v114_n1_p209_Bianco http://hdl.handle.net/20.500.12110/paper_0047259X_v114_n1_p209_Bianco |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Fisher-consistency Generalized linear models Missing data Outliers Robust estimation |
| spellingShingle |
Fisher-consistency Generalized linear models Missing data Outliers Robust estimation Bianco, Ana María Boente, Graciela Lina Resistant estimators in poisson and gamma models with missing responses and an application to outlier detection |
| topic_facet |
Fisher-consistency Generalized linear models Missing data Outliers Robust estimation |
| description |
When dealing with situations in which the responses are discrete or show some type of asymmetry, the linear model is not appropriate to establish the relation between the responses and the covariates. Generalized linear models serve this purpose, since they allow one to model the mean of the responses through a link function, linearly on the covariates. When atypical observations are present in the sample, robust estimators are useful to provide fair estimations as well as to build outlier detection rules. The focus of this paper is to define robust estimators for the regression parameter when missing data possibly occur in the responses. The estimators introduced turn out to be consistent under mild conditions. In particular, resistant methods for Poisson and Gamma models are given. A simulation study allows one to compare the behaviour of the classical and robust estimators, under different contamination schemes. The robustness of the proposed procedures is studied through the influence function, while asymptotic variances are derived from it. Besides, outlier detection rules are defined using the influence function. The procedure is also illustrated by analysing a real data set. © 2012 Elsevier Inc. |
| author |
Bianco, Ana María Boente, Graciela Lina |
| author_facet |
Bianco, Ana María Boente, Graciela Lina |
| author_sort |
Bianco, Ana María |
| title |
Resistant estimators in poisson and gamma models with missing responses and an application to outlier detection |
| title_short |
Resistant estimators in poisson and gamma models with missing responses and an application to outlier detection |
| title_full |
Resistant estimators in poisson and gamma models with missing responses and an application to outlier detection |
| title_fullStr |
Resistant estimators in poisson and gamma models with missing responses and an application to outlier detection |
| title_full_unstemmed |
Resistant estimators in poisson and gamma models with missing responses and an application to outlier detection |
| title_sort |
resistant estimators in poisson and gamma models with missing responses and an application to outlier detection |
| publishDate |
2013 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v114_n1_p209_Bianco http://hdl.handle.net/20.500.12110/paper_0047259X_v114_n1_p209_Bianco |
| work_keys_str_mv |
AT biancoanamaria resistantestimatorsinpoissonandgammamodelswithmissingresponsesandanapplicationtooutlierdetection AT boentegracielalina resistantestimatorsinpoissonandgammamodelswithmissingresponsesandanapplicationtooutlierdetection |
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