On the impact of weights approximation in resampling

ITACOSM 2015 Federico Andreis 1 , Pier Luigi Conti2 , Fulvia Mecatti3

On the impact of weights approximation in resampling based on pseudo-populations

Abstract The practice of rounding non-integer weights in bootstrapping complex samples from nite populations has been empirically shown to be potentially damaging. Indeed, the extent to which rounding can interfere with basic Bootstrap principles as well as with the formal properties of the nal Bootstrap estimates can be non-negligible and often severe. On the basis of these considerations, in our talk we derive asymptotic results that suggest under which conditions the use of rounding can be detrimental, and attempt a quantication of the unwanted eects induced by this practice with respect to some relevant performance indicators for estimators such as, for example, relative bias and relative root mean square error. Empirical results are discussed based on an extended simulative study, accounting for dierent high-entropy π -ps sampling designs in a number of dierent population scenarios.

Essential references [1] Andreis, F., Mecatti, F. (2015) ROUNDING NON-INTEGER WEIGHTS IN BOOTSTRAPPING NON-IID SAMPLES: ACTUAL PROBLEM OR HARMLESS PRACTICE?, Advances in Complex Data Modeling and Computational Methods in Statistics, Springer. [2] Holmberg, A. (1998) A Bootstrap approach to probability proportional to size sampling, in Proceedings of Section on Survery Research Methods , American Statistical Association, 181184.

1 University of Milan, Italy, [email protected] 2 University of Rome-Sapienza, Italy, [email protected]

3 University of Milan-Bicocca,

Italy,

[email protected]

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