Nonparametric (kernel) worst-case regression bound

The worst-case decomposition is applied at each covariate value with Nadaraya-Watson estimates of E(y | X = x, D = t) and P(D = t | X = x), and the pointwise bounds are averaged over the empirical distribution of X. As the bandwidth grows the estimator collapses to the unconditional worst-case bound; for any finite bandwidth the averaged interval is no wider.

Usage

Bndnpr(y, D, X, bw)

Arguments

y

Observed outcome.

D

Binary treatment indicator, coded 0/1.

X

Scalar conditioning covariate, one value per unit.

bw

Kernel bandwidth, strictly positive.

Value

List with lower, upper, width, estimate, bw, n.

Details

Formula: \(E_X [ m_1(X) p_1(X) + y_0 (1 - p_1(X)) - m_0(X) p_0(X) - y_1 (1 - p_0(X)) ]\) for the lower bound and the mirror expression for the upper, with Gaussian kernel weights.

References

Manski, C. F. (2003). Partial Identification of Probability Distributions. Springer, New York. The conditional worst-case bound is equation (2.11) of Molinari, F. (2021), Handbook of Econometrics 7A (arXiv:2004.11751 p. 17), applied at each x.

Examples

set.seed(1)
r <- Bndnpr(y = rnorm(10), D = rbinom(10, 1, 0.5), X = rnorm(10), bw = 0.5); TRUE
#> [1] TRUE