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Local Influence in Regression Models with Measurement Errors and Censored Data Considering the Student–t Distribution

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  • Alejandro Monzón Montoya

    (Universidade Federal de Minas Gerais
    Universidad Nacional de San Cristóbal de Huamanga)

Abstract

In this paper, the local influence approach is studied in regression models with measurement errors for multivariate censored responses under the Student-t distribution. The multivariate Student–t distribution and the multivariate normal, distributions of the independent normal class, are studied and used to compare various measuring instruments. The ECM algorithm is used to obtain maximum likelihood estimates of the model parameters and using the log-likelihood function of the complete data we obtain measures of local influence based on the methodology proposed by Zhu and Lee (Journal of the Royal Statistical Society, Series B 63:121–126, 2001) and Lee and Xu (Computational Statistics and Data Analysis 45:321–341, 2004). Finally, the described methodologies are used in real data analysis that illustrates the usefulness of the approach.

Suggested Citation

  • Alejandro Monzón Montoya, 2024. "Local Influence in Regression Models with Measurement Errors and Censored Data Considering the Student–t Distribution," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 91-108, May.
    • Handle: RePEc:spr:sankhb:v:86:y:2024:i:1:d:10.1007_s13571-023-00316-6
    DOI: 10.1007/s13571-023-00316-6
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    References listed on IDEAS

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    1. Hong‐Tu Zhu & Sik‐Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
    2. V. Lachos & T. Angolini & C. Abanto-Valle, 2011. "On estimation and local influence analysis for measurement errors models under heavy-tailed distributions," Statistical Papers, Springer, vol. 52(3), pages 567-590, August.
    3. W.‐Y. Poon & Y. S. Poon, 1999. "Conformal normal curvature and assessment of local influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 51-61.
    4. Lee, Sik-Yum & Xu, Liang, 2004. "Influence analyses of nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 321-341, March.
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