sup_t |sqrt(n)(F_n(t) - F0(t)) - B(F0(t))| tends to zero almost
surely: the empirical process can be constructed on the SAME
probability space as its Brownian bridge limit, so the two stay
uniformly close rather than merely agreeing in distribution. The
observable consequence is that the sup statistic sits at the
Kolmogorov-Smirnov scale, which is what is computed here.
Usage
Ghosalstrongapxdp(n = 3000, seed = 42)
Arguments
- n
Sample size.
- seed
Seed for the deterministic draws.
Value
List with estimate (the KS statistic),
typical_ks_range, method.
Details
Formula: KS = sqrt(n) sup_i max(|i/n - X_(i)|, |(i-1)/n - X_(i)|)
for the uniform truth.
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 12.2.1.
Examples
Ghosalstrongapxdp()
#> $estimate
#> [1] 0.4520859
#>
#> $typical_ks_range
#> [1] TRUE
#>
#> $method
#> [1] "strong approximation (GvdV 2017 sec. 12.2.1)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
