Hellinger-affinity bound from strong delta-separation at stage k

The stage k divides n, so separating only at a large k gives a correspondingly slower exponential rate.

Usage

Sepcons(delta, k, n)

Arguments

delta

Separation level, 0 < delta < 1.

k

Stage at which separation holds, k >= 1.

n

Sample size.

Value

List with bound, rate, exponent, delta, k, n.

Details

Formula: rho_{1/2}(p_0^n, int p^n dmu(p)) < e^{-(n/k) log_- delta} = delta^{n/k}

References

Ghosal & van der Vaart (2017), Fundamentals of Nonparametric Bayesian Inference, Section 6.8.1: Definition 6.43, Lemma 6.44 and Theorem 6.45. Read from the copy of the book held in the corpus.

Examples

Sepcons(delta = 0.5, k = 5L, n = 5L)
#> $bound
#> [1] 0.5
#> 
#> $rate
#> [1] 0.1386294
#> 
#> $exponent
#> [1] -0.6931472
#> 
#> $delta
#> [1] 0.5
#> 
#> $k
#> [1] 5
#> 
#> $n
#> [1] 5
#> 
#> $method
#> [1] "Strong separation bound, Ghosal Lemma 6.44"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"