Asymptotic properties of (r,s)-directed divergences in a stratified sampling

摘要

An (r,s)-directed divergence statistic is obtained by either replacing both distributions involved in the argument by their sample estimates or replacing one distribution and considering the other as given. Asymptotic properties of (r,s)-directed divergence statistics are investigated in a stratified random sampling with proportional allocation and independence among strata. These results are used in various settings to construct confidence intervals and to test statistical hypotheses based on one or more samples from multinomial populations.