Abstract
In this paper we consider applications of local influence (Cook, 1986) to evaluate small perturbations in the model or in data sets of several measuring devices, assuming Grubbs's model. Different perturbation schemes are investigated and an application is considered to two real data sets.
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References
Barnett, V.D. (1969). Simulataneous pairwise linear structural relationships. Biometrics, 25, 129–142.
Bechman, R., Nachtsheim, C. and Cook, R. (1987). Diagnostics for mixedmodel analysis of variance. Technometrics, 29, 413–426.
Bedrick, E. J. (2001). An efficient scores test for comparing several measuring devices. Journal of Quality Technology, 33, 96–103.
Bolfarine, H. and Galea, M. (1995). Structural comparative calibration using the EM algorithm. Journal of Applied Statistics, 22, 277–292.
Chatterjee, S. and Hadi, A. S. (1988). Sensivity Analysis in Linear Regression, John Wiley, New York.
Christensen, R. and Blackwood, L. (1993). Test for precision and acurracy of multiple measuring devices. Technometrics, 35, 411–420.
Cook, R.D. (1986). Assessment of local influence. Journal of the Royal Statistical Society, B. 48, 133–169.
Cook, R.D. and Weisberg, S. (1982). Residuals and Influence in Regression, Chapman and Hall, London.
Escobar, E. and Meeker, W. (1992). Assessing influence in regression analysis with censored data. Biometrics, 48, 507–528.
Galea, M., Bolfarine, H. and de Castro, M. (2002). Local influence in comparative calibration models. Biometrical Journal, 44, 59–81.
Galea, M., Paula, G.A. and Bolfarine, H. (1997). Local influence in elliptical linear regression models. The Statistician, 46, 71–79.
Grubbs, F.E. (1948). On estimating precision of measuring instruments and product variability. Journal of the American Statistical Association, 43, 243–264.
Grubbs, F.E. (1973). Errors of measurement, precision, accuracy and the statistical comparison of measuring instruments. Technometrics, 15, 53–66.
Grubbs, F.E. (1983). Grubbs's estimator. Encyclopedia of Statistical Sciences, 3, 542–549.
Jaech, J.L. (1985). Statistical analysis of measurement errors. Exxon Monographs. John Wiley, New York.
Kelly, G. (1984). The influence function in the errors in variables problem. The Annals of Statistics, 12, 87–100.
Kwan, C. and Fung, W. (1998). Assessing local influence for specific restricted likelihood: Application to factor analysis. Psychometrika, 63, 35–46.
Lawrance, A.J. (1988). Regression transformation diagnostic using local influence. Journal of the American Statistical Association, 83, 1067–1072.
Lesaffre, E. and Verbeke, G. (1998). Local influence in linear mixed models. Biometrics, 54, 570–583.
Paula, G.A. (1993). Assessing local influence in restricted regressions models. Computational Statistics and Data Analysis, 16, 63–79.
Tanaka, Y., Watadani, S. and Moon, S. (1991). Influence in covariance structure analysis with an application to confirmatory factor analysis. Communitations in Statistics-Theory and Methods, 20, 3805–3821.
Thomas, W. and Cook, R.D. (1990). Assessing influence on predictions from generalized linear models. Technometrics, 32, 59–65.
Tsai, C.L. and Wu, X. (1992). Assessing local influence in linear regression models with first-order autoregressive or heteroscedastic error structure. Statistics and Probability Letters, 14, 247–252.
Verbeke, G. and Molenberghs, G. (2000). Linear mixed models for longitudinal data. Springer, New York.
Zhao, Y. and Lee, A. (1998). Influence diagnostics for simultaneous equations models. Australian and New Zealand Journal Statistics, 40, 345–357.
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Lachos, V.H., Vilca, F. & Galea, M. Influence diagnostics for the Grubbs's model. Statistical Papers 48, 419–436 (2007). https://doi.org/10.1007/s00362-006-0345-4
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DOI: https://doi.org/10.1007/s00362-006-0345-4