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Diagnostics in multivariate generalized Birnbaum-Saunders regression models

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  • Carolina Marchant
  • Víctor Leiva
  • Francisco José A. Cysneiros
  • Juan F. Vivanco

Abstract

Birnbaum–Saunders (BS) models are receiving considerable attention in the literature. Multivariate regression models are a useful tool of the multivariate analysis, which takes into account the correlation between variables. Diagnostic analysis is an important aspect to be considered in the statistical modeling. In this paper, we formulate multivariate generalized BS regression models and carry out a diagnostic analysis for these models. We consider the Mahalanobis distance as a global influence measure to detect multivariate outliers and use it for evaluating the adequacy of the distributional assumption. We also consider the local influence approach and study how a perturbation may impact on the estimation of model parameters. We implement the obtained results in the R software, which are illustrated with real-world multivariate data to show their potential applications.

Suggested Citation

  • Carolina Marchant & Víctor Leiva & Francisco José A. Cysneiros & Juan F. Vivanco, 2016. "Diagnostics in multivariate generalized Birnbaum-Saunders regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2829-2849, November.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:15:p:2829-2849
    DOI: 10.1080/02664763.2016.1148671
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    1. Miguel Angel Uribe-Opazo & Joelmir Andr� Borssoi & Manuel Galea, 2012. "Influence diagnostics in Gaussian spatial linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(3), pages 615-630, July.
    2. V�ctor Leiva & Carolina Marchant & Helton Saulo & Muhammad Aslam & Fernando Rojas, 2014. "Capability indices for Birnbaum-Saunders processes applied to electronic and food industries," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 1881-1902, September.
    3. Caro-Lopera, Francisco J. & Leiva, Víctor & Balakrishnan, N., 2012. "Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 126-139, February.
    4. Nedret Billor, 1999. "An application of the local influence approach to ridge regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(2), pages 177-183.
    5. Michelli Barros & Manuel Galea & Manuel González & Víctor Leiva, 2010. "Influence diagnostics in the tobit censored response model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 379-397, August.
    6. Marco Riquelme & V�ctor Leiva & Manuel Galea & Antonio Sanhueza, 2011. "Influence diagnostics on the coefficient of variation of elliptically contoured distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(3), pages 513-532, November.
    7. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "A robust extension of the bivariate Birnbaum–Saunders distribution and associated inference," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 418-435.
    8. Kundu, Debasis & Balakrishnan, N. & Jamalizadeh, Ahad, 2013. "Generalized multivariate Birnbaum–Saunders distributions and related inferential issues," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 230-244.
    9. V�ctor Leiva & Emilia Athayde & Cecilia Azevedo & Carolina Marchant, 2011. "Modeling wind energy flux by a Birnbaum--Saunders distribution with an unknown shift parameter," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2819-2838, February.
    10. R.A.B. Assumpção & M.A. Uribe-Opazo & M. Galea, 2014. "Analysis of local influence in geostatistics using Student's t -distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2323-2341, November.
    11. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
    12. Manuel Galea & Victor Leiva-Sanchez & Gilberto Paula, 2004. "Influence Diagnostics in log-Birnbaum-Saunders Regression Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(9), pages 1049-1064.
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    Cited by:

    1. Alejandra Tapia & Victor Leiva & Maria del Pilar Diaz & Viviana Giampaoli, 2019. "Influence diagnostics in mixed effects logistic regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 920-942, September.
    2. Michelli Barros & Manuel Galea & Víctor Leiva & Manoel Santos-Neto, 2018. "Generalized Tobit models: diagnostics and application in econometrics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 145-167, January.
    3. Mário Fernando De Sousa & Helton Saulo & Víctor Leiva & Paulo Scalco, 2018. "On Some Properties Of A New Asymmetry-Based Tobit Model," Anais do XLIV Encontro Nacional de Economia [Proceedings of the 44th Brazilian Economics Meeting] 129, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    4. Camilo Lillo & Víctor Leiva & Orietta Nicolis & Robert G. Aykroyd, 2018. "L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(2), pages 187-209, January.
    5. Aline B. Tsuyuguchi & Gilberto A. Paula & Michelli Barros, 2020. "Analysis of correlated Birnbaum–Saunders data based on estimating equations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 661-681, September.
    6. Luis Sánchez & Víctor Leiva & Manuel Galea & Helton Saulo, 2020. "Birnbaum-Saunders Quantile Regression Models with Application to Spatial Data," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    7. Rodrigo Puentes & Carolina Marchant & Víctor Leiva & Jorge I. Figueroa-Zúñiga & Fabrizio Ruggeri, 2021. "Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model," Mathematics, MDPI, vol. 9(6), pages 1-24, March.
    8. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    9. Víctor Leiva & Helton Saulo & Rubens Souza & Robert G. Aykroyd & Roberto Vila, 2021. "A new BISARMA time series model for forecasting mortality using weather and particulate matter data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 346-364, March.

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