Quantile-stratified sampling, one draw from each equal-probability quantile block, makes empirical quantiles track the true quantiles more closely than IID sampling and can reduce importance-sampling error.
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One-dimensional quantile-stratified sampling and its application in statistical simulations
Quantile-stratified sampling, one draw from each equal-probability quantile block, makes empirical quantiles track the true quantiles more closely than IID sampling and can reduce importance-sampling error.