Standard error, interval and score check from an influence curve

An efficient influence curve must have empirical mean ZERO at the targeted estimate; score_solved reports whether it does, because if it does not the standard error is not trustworthy.

Usage

Tmleinf(psi, ic, level = 0.95, null_value = 0)

Arguments

psi

The targeted point estimate.

ic

Influence-curve values, one per observation.

level

Confidence level.

null_value

Value tested against.

Value

List with estimate, se, ci_lower, ci_upper, statistic, p_value, ic_mean, score_solved, n.

Details

Formula: se = sqrt(var(IC)/n); CI = psi -+ z_{alpha/2} se; the estimating equation is (1/n) sum IC_i = 0

References

Verified against the CRAN package tmle 2.1.1 (Gruber & van der Laan), whose calcParameters computes var.psi <- var(IC)/n, the qnorm-based interval and pvalue <- 2*pnorm(-abs(psi/sqrt(var.psi))).

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Tmleinf(V, V)
#> $estimate
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $se
#> [1] 0.8660254
#> 
#> $ci_lower
#> [1] -0.6973786  0.3026214  1.3026214  2.3026214  3.3026214  4.3026214  5.3026214
#> [8]  6.3026214
#> 
#> $ci_upper
#> [1] 2.697379 3.697379 4.697379 5.697379 6.697379 7.697379 8.697379 9.697379
#> 
#> $statistic
#> [1] 1.154701 2.309401 3.464102 4.618802 5.773503 6.928203 8.082904 9.237604
#> 
#> $p_value
#> [1] 2.482131e-01 2.092134e-02 5.320055e-04 3.859616e-06 7.764037e-09
#> [6] 4.262192e-12 6.324253e-16 2.520778e-20
#> 
#> $ic_mean
#> [1] 4.5
#> 
#> $score_solved
#> [1] 0
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Influence-curve inference for a targeted estimate"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"