Abstract
Jittered Sampling is a refinement of the classical Monte Carlo sampling method. Instead of picking $n$ points randomly from $[0,1]^2$, one partitions the unit square into $n$ regions of equal measure and then chooses a point randomly from each partition. Currently, no good rules for how to partition the space are available. In this paper, we present a solution for the special case of subdividing the unit square by a decreasing function into two regions so as to minimize the expected squared $\mathcal{L}_2$discrepancy. The optimal partitions are given by a \textit{highly} nonlinear integral equation for which we determine an approximate solution. In particular, there is a break of symmetry and the optimal partition is not into two sets of equal measure. We hope this stimulates further interest in the construction of good partitions.
Original language  English 

Pages (fromto)  5561 
Journal  Statistics & Probability Letters 
Volume  132 
Early online date  27 Sep 2017 
DOIs  
Publication status  Published  01 Jan 2018 
Keywords
 math.NA
 math.OC
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Florian Pausinger
 School of Mathematics and Physics  Visiting Scholar
 Mathematical Sciences Research Centre
Person: Academic