Asymptotic Normality and the Bootstrap in Stratified Sampling

摘要: This paper is about the asymptotic distribution of linear combinations stratum means in stratified sampling, with and without replacement. Both number strata their size arbitrary. Lindeberg conditions are shown to guarantee normality consistency variance estimators. The same also validity bootstrap approximation for $t$-statistic. Via a bound on Mallows distance, situations will be identified which works even though normal fails. Without proper scaling, naive