Worst-case bias bound under local misspecification

|bias| <= c ||s||_2 by Cauchy-Schwarz, attained at gamma = c s / ||s||, and the conservative interval is estimate +/- (c ||s|| + z_{1-alpha/2} se).

Usage

Misspecbd(estimate, sensitivity, c, se, conf = 0.95)

Arguments

estimate: Point estimate under the baseline model.
sensitivity: Derivative of the estimate w.r.t. the perturbation.
c: Radius of the misspecification neighbourhood.
se: Standard error under the baseline model.
conf: Nominal confidence level.

Value

List with bias, lower, upper, halfwidth, worstgamma, normsens, z, c.

References

Bias bound by Cauchy-Schwarz; the bias-aware interval is Armstrong and Kolesar (2021), Quantitative Economics 12(1), 77-108, Sect. 2. It is sometimes attributed to Andrews and Kasy (2019), which is about publication bias and is not the source.

Examples

Misspecbd(estimate = 0.5, sensitivity = c(0.1, 0.2), c = 0.3, se = 0.1)
#> $bias
#> [1] 0.06708204
#> 
#> $lower
#> [1] 0.2369216
#> 
#> $upper
#> [1] 0.7630784
#> 
#> $halfwidth
#> [1] 0.2630784
#> 
#> $worstgamma
#> [1] 0.1341641 0.2683282
#> 
#> $normsens
#> [1] 0.2236068
#> 
#> $z
#> [1] 1.959964
#> 
#> $c
#> [1] 0.3
#> 
#> $method
#> [1] "Conservative bias-aware interval under local misspecification"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"