EffBounds: Efficiency bounds under ell_p constraints

In kolesarm/GMMSensitivity: Optimal Sensitivity Analysis in Generalized Method of Moments Models

Description

Computes the asymptotic efficiency of two-sided fixed-length confidence intervals at c=0, as well as the efficiency of one-sided confidence intervals that optimize a given beta quantile of excess length, when the set \mathcal{C} is characterized by \ell_p constraints.

Usage

EffBounds(eo, B, M, p = 2, beta = 0.5, alpha = 0.05)

Arguments

eo	List containing initial estimates with the following components: Sig Estimate of variance of the moment condition, matrix with dimension d_g by d_g, where d_g is the number of moments G Estimate of derivative of the moment condition, matrix with dimension d_g by d_theta, where d_theta is the dimension of theta H Estimate of derivative of h(theta). A vector of length d_theta n sample size g_init Moment condition evaluated at initial estimate
B	matrix B with full rank and dimension d_g by d_gamma that determines the set \mathcal{C}, where d_gamma is the number of invalid moments, and d_g is the number of moments
M	Bound on the norm of gamma
p	Parameter determining which lp norm to use, must equal 1, 2, or Inf.
beta	Quantile of excess length that a one-sided confidence interval is optimizing.
alpha	determines confidence level, 1-alpha, for constructing/optimizing confidence intervals.

Details

The set \mathcal{C} takes the form B*gamma where the lp norm of gamma is bounded by M.

Value

A list with two elements, "onesided" for efficiency of one-sided CIs and "twosided" for efficiency of two-sided CIs

References

Armstrong, T. B., and M. Kolesár (2020): Sensitivity Analysis Using Approximate Moment Condition Models, https://arxiv.org/abs/1808.07387

Examples

## Replicates first line of Table 2 in Armstrong and Kolesár (2020)
## First compute matrix B
I <- vector(mode="logical", length=nrow(blp$G))
I[6] <- TRUE
B <- (blp$ZZ %*% diag(sqrt(blp$n)*abs(blp$perturb)/blp$sdZ))[, I, drop=FALSE]
eo <- list(H=blp$H, G=blp$G, Sig=solve(blp$W), n=blp$n, g_init=blp$g_init)
EffBounds(eo, B, M=1, p=Inf, beta=0.5, alpha=0.05)

kolesarm/GMMSensitivity documentation built on Sept. 17, 2020, 5:47 p.m.