Manski no-assumptions identification bound for a mean

With observation probability p and bounded outcomes [g0, g1], the identification region for E[y] is [m p + g0 (1-p), m p + g1 (1-p)] with m the observed-subsample mean; the width is exactly (g1 - g0)(1 - p).

Usage

morie_bdtrns(y_obs, p_obs, y_lo, y_hi)

Arguments

y_obs

Observed outcomes.

p_obs

Observation probability in [0, 1].

y_lo, y_hi

Logical outcome bounds.

Value

A list with elements lower, upper, width, observed_mean, p_obs, method.

References

Manski, C. F. (2007). Identification for Prediction and Decision. Harvard University Press.

Examples

morie_bdtrns(y_obs = c(1, 0, 1), p_obs = 0.6, y_lo = 0, y_hi = 1)
#> $lower
#> [1] 0.4
#> 
#> $upper
#> [1] 0.8
#> 
#> $width
#> [1] 0.4
#> 
#> $observed_mean
#> [1] 0.6666667
#> 
#> $p_obs
#> [1] 0.6
#> 
#> $method
#> [1] "Manski (2007) worst-case bound (Eqs. 2.8-2.9)"
#>