Comment: Models are approximations! (English) Zbl 1440.62023
Summary: This discussion focuses on areas of disagreement with the papers, particularly the target of inference and the case for using the robust ‘sandwich’ variance estimator in the presence of moderate mis-specification. We also suggest that existing procedures may be appreciably more powerful for detecting mis-specification than the authors’ RAV statistic, and comment on the use of the pairs bootstrap in balanced situations.
Comment on the papers [A. Buja et al., ibid. 34, No. 4, 523–544 (2019; Zbl 1440.62020); ibid. 34, No. 4, 545–565 (2019; Zbl 1440.62021)].
Comment on the papers [A. Buja et al., ibid. 34, No. 4, 523–544 (2019; Zbl 1440.62020); ibid. 34, No. 4, 545–565 (2019; Zbl 1440.62021)].
MSC:
| 62A01 | Foundations and philosophical topics in statistics |
| 62F40 | Bootstrap, jackknife and other resampling methods |
| 62J20 | Diagnostics, and linear inference and regression |
Keywords:
bootstrap; designed experiment; infinitesimal jackknife; model mis-specification; regression diagnostics; sandwich variance estimatorSoftware:
bootlibReferences:
| [1] | Cook, R. D. and Weisberg, S. (1983). Diagnostics for heteroscedasticity in regression. Biometrika 70 1-10. · Zbl 0502.62063 · doi:10.1093/biomet/70.1.1 |
| [2] | Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and Their Application. Cambridge Series in Statistical and Probabilistic Mathematics 1. Cambridge Univ. Press, Cambridge. · Zbl 0886.62001 |
| [3] | Efron, B. and Stein, C. (1981). The jackknife estimate of variance. Ann. Statist. 9 586-596. · Zbl 0481.62035 · doi:10.1214/aos/1176345462 |
| [4] | Fernholz, L. T. (1983). Von Mises Calculus for Statistical Functionals. Lecture Notes in Statistics 19. Springer, New York. · Zbl 0525.62031 |
| [5] | Fisher, R. A. (1935). The Design of Experiments. Oliver and Boyd, Edinburgh. |
| [6] | Fox, T., Hinkley, D. and Larntz, K. (1980). Jackknifing in nonlinear regression. Technometrics 22 29-33. · Zbl 0438.62053 · doi:10.2307/1268380 |
| [7] | Hampel, F. R. (1974). The influence curve and its role in robust estimation. J. Amer. Statist. Assoc. 69 383-393. · Zbl 0305.62031 · doi:10.1080/01621459.1974.10482962 |
| [8] | Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. and Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions. Wiley, New York. · Zbl 0593.62027 |
| [9] | Hinkley, D. V. (1977). Jacknifing in unbalanced situations. Technometrics 19 285-292. · Zbl 0367.62085 · doi:10.1080/00401706.1977.10489550 |
| [10] | Hinkley, D. V. and Wang, S. (1991). Efficiency of robust standard errors for regression coefficients. Comm. Statist. Theory Methods 20 1-11. |
| [11] | Kalbfleisch, J. D. (1975). Sufficiency and conditionality. Biometrika 62 251-268. · Zbl 0313.62004 · doi:10.1093/biomet/62.2.251 |
| [12] | Panaretos, V. M., Kraus, D. and Maddocks, J. H. (2010). Second-order comparison of Gaussian random functions and the geometry of DNA minicircles. J. Amer. Statist. Assoc. 105 670-682. · Zbl 1392.62162 · doi:10.1198/jasa.2010.tm09239 |
| [13] | Tukey, J. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
