The plug-in var(IC) has its own sampling error that a confidence interval built on it treats as zero. Targeting sigma^2 gives it an influence curve D*^2 - sigma^2 and therefore its own interval, on the LOG scale because a variance is positive.
Value
List with sigma2, se_sigma2, ci_lower,
ci_upper, se_psi, se_psi_lower,
se_psi_upper, kurtosis, ic_mean, n.
Details
Formula: sigma^2 = E[D*(O)^2]; IC = D*(O)^2 - sigma^2; se(sigma^2) = sqrt(var(D*^2)/n); se(psi) = sqrt(sigma^2/n)
References
van der Laan, Hubbard and Pajouh (2018), for the problem. What is implemented is the standard construction that follows from the definition: the influence curve of sigma^2 = E[D*^2] is D*^2 - sigma^2. The plug-in variance it refines is the var.psi <- var(IC)/n of the CRAN package tmle 2.1.1 (Gruber & van der Laan).
Examples
V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Tmlevar(V)
#> $sigma2
#> [1] 25.5
#>
#> $se_sigma2
#> [1] 7.98436
#>
#> $ci_lower
#> [1] 13.80444
#>
#> $ci_upper
#> [1] 47.10443
#>
#> $se_psi
#> [1] 1.785357
#>
#> $se_psi_lower
#> [1] 1.313604
#>
#> $se_psi_upper
#> [1] 2.426531
#>
#> $kurtosis
#> [1] 1.686275
#>
#> $ic_mean
#> [1] 4.5
#>
#> $n
#> [1] 8
#>
#> $method
#> [1] "Variance targeting: sigma^2 = E[D*^2] with its own IC"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"