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9.3f. Table 9.3 is similar to Table 3.1 in Dodge (1984). The LS and LAD residuals are displayed in the earlier table. The Huber estimates in the two tables are different because the earlier table used k = 1.345 rather than k = 1.5. 9.3g. Analysis of a data set by more than one method is recommended by Hogg (1979) and Tukey (1991).
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Alam, K., and J. S. Hawkes (1978). Estimation of regression coefficients. ScandanaI'ian Journal of Statistics, vol. 5, pp. 169-172. Arnold, S. F. (1981). The Theory of Linear Models and Multivariate Analysis. Wiley, New York. Barnett, V. (1982). Comparative Statistical Inference, 2nd ed. Wiley,. New York. Bassett, G. Jr., and R. Koenker (1978). Asymptotic theory of least absolute error regression. Journal of the American Statistical Association, vol. 73, pp. 618-622. Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis, 2nd ed. Springer-Verlag, New York. Bickel, P. J. (1965). On some robust estimates of location. Annals of Mathematical Statistics, vol. 36, pp. 847-858. Bloomfield, P., and W. L. Steiger (1983). Least-Absolute Deviations: Theory, Applications, and Algorithms. Birkhauser, Boston. Brownlee, K. A. (1965). Statistical Theory and Methodology in Science and Engineering, 2nd ed. Wiley, New York. Daniel, c., and F. S. Wood (1980). Fitting Equations to Data, 2nd ed. Wiley, New York. Dodge, Y. (1984). Robust estimation of regression coefficients by minimizing a convex combination of least squares and least absolute deviations. Computational Statistics Quarterly, vol. I, pp. 139-153. Field, C. A., and E. M. Ronchetti (1991). An overview of small sample asymptotics. In: W. Stahel and S. Weisberg (eds.), Directions in Robust Statistics and Diagnostics, Part I. Springer-Verlag, New York. Hampel, F. R., E. M. Ronchetti, P. J. Rousseeuw, and W. A. Stahel (1986). Robust Statistics: The Approach Based on Influence Functions. Wiley, New York. Henderson, C. R. (1975). Best linear unbiased estimation and prediction under a selection model. Biometrics, vol. 31, pp. 423-447. Hettmansperger, T. P. (1984). Statistical Inference Based on Ranks. Wiley, New York. Hoerl, A. E., and R. W. Kennard (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics, vol. 12, pp. 55-67. Hogg, R. V. (1979). Statistical robustness: one view of its use in applications today. American Statistician, vol. 33, pp. 108-115. Huber, P. J. (1981). Robust Statistics. Wiley, New York.
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Huber, P. 1. (1987). The place of the L,-norm in robust estimation. In: Y. Dodge (ed.), Statistical Data Analysis Based on the L,-Norm and Related Methods. North-Holland, New York. Lehmann, E. L. (1975). Nonparametrics: Statistical Methods Based on Ranks. HoldenDay, San Francisco. Lehmann, E. L. (1983). Theory of Point Estimation. Wiley, New York. Lehmann, E. L. (1986). Testing Statistical Hypotheses, 2nd ed. Wiley, New York. McKean, 1. W., and S. 1. Sheather (1991). Small sample properties of robust analyses of linear models based on R-estimates: a survey. In: W. Stahel and S. Weisberg (eds.), Directions in Robust Statistics and Diagnostics, Part II. Springer-Verlag, New York. Pfaffenberger, R. c., and T. E. Dielman (1990). A comparison of regression estimators when both multicollinearity and outliers are present. In: K. D. Lawrence and 1. L. Arthur (eds.), Robust Regression: Analysis and Applications. Marcel Dekker, New York. Press, S. 1. (1989). Bayesian Statistics: Principles, Models, and Applications. Wiley, New York. Schrader, R. M., and 1. W. McKean (1987). Small sample properties of least absolute errors analysis of variance. In: Y. Dodge (ed.), Statistical Data Analysis Based on the LJ-Norm and Related Methods. North-Holland, New York. Schrader, R. M., and T. P. Hettmansperger (1980). Robust analysis of variance based on a likelihood criterion. Biometrika, vol. 67, pp. 93-101. Tukey, 1. W. (1991). Graphical displays for alternate regression fits. In: W. Stahel and S. Weisberg (eds.), Directions in Robust Statistics and Diagnostics, Part II. Springer-Verlag, New York. Weisberg, S. (1985). Applied Linear Regression, 2nd ed. Wiley, New York.
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