Abstract
The paper studies S-weighted estimator - a combination of S-estimator and the least weighted squares. The estimator allows to adjust the properties, namely the level of robustness of estimator in question to the processed data better than the S-estimator or the least weighted squares can do. The paper offers the proof of its \(\sqrt{n}\)-consistency.
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- 1.
That is why that although LTS was defined in eighties, the general proofs of its properties appeared as late as in 2006, see [16].
- 2.
It is clear from Fig. 1 that any estimator with high breakdown point generally suffer by “switch effect” but the Engine Knock Data indicate that it can happen for much lower breakdown point.
- 3.
HP Elite 7500 with Intel Core i7-3770 Processor (3.4 GHz, 8 MB cache).
- 4.
We experimented with various numbers of repetitions - smaller than 100 exhibited some instability in MSE, in the sense that repeated simulations (yielding one particular table - see below) gave (rather) different information about the dispersion of the estimates for individual datasets, - the number of repetitions larger than 100 gave a lower information about the preciseness of estimation by \(\hat{\beta }^{(method)}_j\) (see (14)) just resulting in exact “true values of coefficients”, see (13).
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Acknowledgements
This paper was written with the support of the Czech Science Foundation project No. P402/12/G097 DYME Dynamic Models in Economics.
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Appendix
Appendix
See Fig. 2.
Examples of the weight function of Tukey’s shape for SW-estimator. Experiences from simulations hint that under the serious heteroscedasticity the left-hand side weight function gives better results
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Víšek, J.Á. (2019). Asymptotics of S-Weighted Estimators. In: Crocetta, C. (eds) Theoretical and Applied Statistics. SIS 2015. Springer Proceedings in Mathematics & Statistics, vol 274. Springer, Cham. https://doi.org/10.1007/978-3-030-05420-5_4
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