By D. A. Freedman, W. Navidi, S. C. Peters (auth.), Dr. Theo K. Dijkstra (eds.)
In this e-book difficulties regarding the alternative of versions in such varied fields as regression, covariance constitution, time sequence research and multinomial experiments are mentioned. The emphasis is at the statistical implications for version evaluation while the evaluate is completed with an identical information that generated the version. it is a challenge of lengthy status, infamous for its hassle. a few members speak about this challenge in an illuminating approach. Others, and this can be a actually novel characteristic, examine systematically no matter if pattern re-use tools just like the bootstrap can be utilized to evaluate the standard of estimators or predictors in a competent means given the preliminary version uncertainty. The ebook may still turn out to be helpful for complex practitioners and statistical methodologists alike.
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Additional info for On Model Uncertainty and its Statistical Implications: Proceedings of a Workshop, Held in Groningen, The Netherlands, September 25–26, 1986
Example text
Journal of Econometrics 25, 35-48. , 1978, Specification searches. Ad hoc inference with non-experimental data (Wiley, New York). , 1983, Data mining, Review of Economics and Statistics 65, 1-12. Nakamura, A. and M. Nakamura, 1978, On the impact of the tests for serial correlation upon the test of significance for the regression coefficient, Journal of Econometrics 7, 199-210. Rao, P. and Z. Griliches, 1969, Small-sample properties of several two-stage regression methods in the context of autocorrelated errors, Journal of the American Statistical Association 64, 253-272.
A "predl ctor error approach" is followed. as discussed in Ljung and S~derstr~ (1983). Some "conventional" and "cross-valIdatory" procedures are proposed. and their performance is compared In a simulation study. The cross-validatory procedures are based on realIzed predIction errors in the past. The conventional procedures seem to perform. on the average. at least as well as the cross-valIdatory procedures. * This research was carried out when the author was at the InstItute of Econometrics of the University of Groningen.
Similar tables are constructed for a = 1 and a = log n. There appear to be a few patterns to discern. On the average. the absolute bias is underestimated. the standard errors and the correlation are overestimated. (The medians offer if anything a slightly improved picture). Perhaps this can also be attributed to the fact that the bootstrap-samples favor the full model disproportionately: the bootstrap tends to mimic the sampling distribution of b. This distribution has the correct means and the variances are larger than :hose 8i -8 i ; in addition b l and b2 are more strongly correlated than 81 and 82 • As with the selection probabilities one might expect a better 0: performance when in case xl is selected the bootstrap samples are constructed from e l • 5.