. Finally, 000 from the uniform distribution over the square (?2, 2) 2 . The function choice.grid was applied to these samples with N=30 and ng=1. The resulting couple of initial and optimal grids are plotted in Figure 7. As in the univariate case, we observe an improvement when going from the initial grids to the corresponding optimal grids provided by the function choice.grid (here as well, the population optimal grid should be uniformly spread over the support of the underlying distribution)

. Also, set.seed(345689) n <-2222 X <-matrix(runif(n*2, -2, 2), nc = n) N <-33 ng <-1 res <-choice.grid(X, N, ng) col <-c("red, res$init_grid, p.col

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