sqrt(n)(psi(F_post) - psi(F0)) tends to N(0, sigma^2) for smooth
functionals of an NTR posterior. With psi = F(1) under an
uncensored exponential truth the limiting variance is
F0(1)(1 - F0(1)), the same bound a fully parametric analysis would
give – the nonparametric prior costs nothing for this functional.
Usage
Ghosalntrbvm(n = 1500, n_sim = 300, seed = 42)
Arguments
- n
Sample size per replicate.
- n_sim
Number of replicates.
- seed
Seed for the deterministic draws.
Value
List with estimate (empirical variance),
efficient_variance, gap, method.
Details
Formula: F_post(1) = (2 F0(1) + N_1) / (2 + n);
Var(sqrt(n)(F_post(1) - F0(1))) -> F0(1)(1 - F0(1)).
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 13.4.2.
Examples
# \donttest{
Ghosalntrbvm()
#> $estimate
#> [1] 0.2443214
#>
#> $efficient_variance
#> [1] 0.2325442
#>
#> $gap
#> [1] 0.01177723
#>
#> $method
#> [1] "NTR functional BvM (GvdV 2017 sec. 13.4.2)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
# }
