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When stratification, cluster sampling or probability weights are introduced into sampling this assumption is violated and the bootstrap as described above will give incorrect inferences.
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In other words, the received signal is stationary with the observation time T (i.e., N s samples); this assumption is commonly used in the literature [29 32].
Finally, homogeneity of regression slopes was assessed; for some analyses for the ITT sample this assumption was violated.
However, for individual studies with sufficient samples, this assumption can be relaxed by using gene-specific variances s instead of in (1).
Manual inspection of samples confirmed this assumption.
The fact that the association between moderate/severe periodontitis and psoriasis was attenuated when smoking was entered into the regression model for the whole sample supports this assumption.
However, with our reduced sample size, this assumption is not supported: half of the cases of compensation are associated to SE or RSE while the other half corresponds to cases of ME.
Currently the most common estimation methods assume observations are sampled using a probabilistic sampling scheme, however this assumption is often not met.
First, theoretical results in Politis et al. [ 1999, pp. 47 51] suggest that subsampling is less efficient but more general than bootstrapping; specifically, that whereas bootstrap methods must often assume that the estimated statistic is at least locally smooth (which the true or sampled is not), this assumption is not needed for subsampling.
Although most algorithms are robust to minor violations of this assumption, sampling bias in the case of genetic datasets may be too large for algorithms to accurately recover stratification.
The calculation of CIQs has traditionally been based on the large-sample assumption that the quantile estimators are normally distributed, but with small samples commonly available, this assumption is shown to be quite crude.
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