Chernozhukov-Lee-Rosen intersection bounds with independent cells

The target is the minimum over cells of the conditional means. Each cell is precision-corrected before the minimum is taken, \(\hat\theta(p) = \min_{v \in \hat V} (m_v + k_{\hat V}(p) s_v)\), where for independent cells \(k_S(p) = \Phi^{-1}(p^{1/|S|})\) is the p-quantile of the maximum of \(|S|\) independent standard normals and the contact set keeps the cells with \(m_v \le \min_u (m_u + k_V(\gamma_n) s_u) + 2 k_V(\gamma_n) s_v\), \(\gamma_n = 1 - 0.1/\log n\). Identical to the Python arm morie.fn.chrbnd.chernozhukov_rosen_bounds. (This function used to subtract a multiple of the standard error, the wrong direction.)

Usage

Chrbnd(y, X = NULL, instrument = NULL, alpha = 0.05, gamma = NULL, beta = 0.1)

Arguments

y

Numeric outcome.

X

Ignored (signature parity).

instrument

Cell label per observation; NULL is one cell.

alpha

One-sided level of the upper confidence bound.

gamma

Contact-set level; default \(1 - 0.1/\log n\).

beta

Unused (signature parity).

Value

A list with estimate and bound (the one-sided upper confidence bound), hmu_estimate (half-median-unbiased), naive_min, cells, means, ses, contact_set (zero-based), k_alpha, k_gamma, n_cells, n and method.

References

Chernozhukov, V., Lee, S. and Rosen, A. M. (2013). Intersection bounds: estimation and inference. Econometrica 81, 667-737.

Examples

Chrbnd(c(3, 3.5, 2.8, 1, 1.6, 1.2, 5, 4.1),
  instrument = c(0, 0, 0, 1, 1, 1, 2, 2))$bound
#> [1] 1.556792