Pi_n(F : d(F, F0) > eps | data) tends to zero under a KL-type support
condition on the NTR prior. Consistency under CENSORING is the point:
the observed information about F is only partial, and the theorem says
the prior still washes out. The demonstration runs the Bayesian
product-limit estimator under light censoring and watches its error at
t = 1 fall with n.
Usage
Ghosalntrconsist(ns = c(100, 800, 6400), seed = 42)
Arguments
- ns
Increasing vector of sample sizes.
- seed
Seed for the deterministic draws.
Value
List with estimate (error at the largest n),
err_by_n, improving, method.
Details
Formula: S(1) = prod over events t_j <= 1 of
(R_j - 1 + 2 exp(-t_j)) / (R_j + 2 exp(-t_j)); target exp(-1).
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 13.4.1.
Examples
Ghosalntrconsist()
#> $estimate
#> [1] 0.005058324
#>
#> $err_by_n
#> [1] 0.065041597 0.008475249 0.005058324
#>
#> $improving
#> [1] TRUE
#>
#> $method
#> [1] "NTR consistency (GvdV 2017 sec. 13.4.1)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
