Certify that a test sequence has exponentially small error probabilities

The rate is read off a single n, so it is a certificate at that n and not a proof of a rate.

Usage

Exptest(err_null, err_alt, n)

Arguments

err_null

Type I error, in (0, 1].

err_alt

Worst-case type II error, in (0, 1].

n

Sample size at which the errors were observed.

Value

List with rate, rate_null, rate_alt, bound, exponential, n.

Details

Formula: C_0 = -log(P_0^n phi_n)/n, C_1 = -log(sup P^n(1 - phi_n))/n, C = min(C_0, C_1)

References

Ghosal & van der Vaart (2017), Fundamentals of Nonparametric Bayesian Inference, Theorem 6.16 (Schwartz) and its proof, which invokes Lemma D.11. Read from the copy of the book held in the corpus.

Examples

Exptest(err_null = 0.1, err_alt = 0.2, n = 100)
#> $rate
#> [1] 0.01609438
#> 
#> $rate_null
#> [1] 0.02302585
#> 
#> $rate_alt
#> [1] 0.01609438
#> 
#> $bound
#> [1] 0.2
#> 
#> $exponential
#> [1] 1
#> 
#> $n
#> [1] 100
#> 
#> $method
#> [1] "Exponential test-consistency rate, Ghosal Theorem 6.16"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"