Criterion-function set estimate for moment inequalities

Q_n(theta) = sum_j [max(mbar_j/sigma_j, 0)]^2 and C_n = {theta : n Q_n(theta) <= cutoff}.

Usage

Qcritset(mbar, se = NULL, n = 1, cutoff = NULL)

Arguments

mbar

Sample moment means, one row per candidate theta.

se

Moment standard deviations, length J or the shape of mbar.

n

Sample size behind the moment means.

cutoff

Level-set cutoff; NULL uses min(n Q_n).

Value

List with Q, nQ, argmin (zero-based), minQ, inset, nin, cutoff, g, J.

References

Chernozhukov, Hong and Tamer (2007), Econometrica 75(5), 1243-1284, Sect. 2; standard published form.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Qcritset(V)
#> $Q
#> [1]  1  4  9 16 25 36 49 64
#> 
#> $nQ
#> [1]  1  4  9 16 25 36 49 64
#> 
#> $argmin
#> [1] 0
#> 
#> $minQ
#> [1] 1
#> 
#> $inset
#> [1] 1 0 0 0 0 0 0 0
#> 
#> $nin
#> [1] 1
#> 
#> $cutoff
#> [1] 1
#> 
#> $g
#> [1] 8
#> 
#> $J
#> [1] 1
#> 
#> $method
#> [1] "Criterion-function set estimate (Chernozhukov-Hong-Tamer 2007)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"