Test a null value against the Imbens-Manski confidence interval

The decision is whether the interval that covers the true parameter with probability 1 - alpha contains theta_0. The critical value is the one already implemented in morie_bnd_imbens_manski and reached through Bndfre; nothing about the construction is re-derived here.

Usage

Bnstst(lower, upper, se = 0, cdf = 0.05)

Arguments

lower, upper

Replicated estimates of the two bounds, same length.

se

The null value theta_0, default 0.

cdf

The level alpha, default 0.05.

Value

List with lower, upper, width, covers, reject, c, theta_0, n.

Note

the parameter names se and cdf are inherited generator boilerplate, kept so existing positional calls do not break; they carry the meanings documented above. Stoye's (2009) refinement, which pre-tests the width of the estimated bounds and switches between a one- and a two-sided critical value, is NOT implemented: its pre-test threshold could not be verified against an accessible copy.

References

Imbens, G. W. and Manski, C. F. (2004). Confidence intervals for partially identified parameters. Econometrica 72(6), 1845-1857, equation (6). doi:10.1111/j.1468-0262.2004.00555.x . Stoye, J. (2009). More on confidence intervals for partially identified parameters. Econometrica 77(4), 1299-1315. doi:10.3982/ECTA7347 .

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Bnstst(V, V)
#> $lower
#> [1] 2.802621
#> 
#> $upper
#> [1] 6.197379
#> 
#> $width
#> [1] 3.394757
#> 
#> $covers
#> [1] 0
#> 
#> $reject
#> [1] 1
#> 
#> $c
#> [1] 1.959964
#> 
#> $theta_0
#> [1] 0
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Inference on an interval-identified parameter"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"