Estimation of the Population Average Value in Randomized Experiments Under Cross Validation

This function estimates the Population Average Value. The details of the methods for this design are given in Imai and Li (2019).

Usage

PAVcv(T, That, Y, ind, centered = TRUE)

Arguments

T

A vector of the unit-level binary treatment receipt variable for each sample.

That

A matrix where the ith column is the unit-level binary treatment that would have been assigned by the individualized treatment rule generated in the ith fold. If budget is specified, please ensure that the percentage of treatment units of That is lower than the budget constraint.

Y

The outcome variable of interest.

ind

A vector of integers (between 1 and number of folds inclusive) indicating which testing set does each sample belong to.

centered

If TRUE, the outcome variables would be centered before processing. This minimizes the variance of the estimator. Default is TRUE.

Value

A list that contains the following items:

pav

The estimated Population Average Value.

sd

The estimated standard deviation of PAV.

References

Imai and Li (2019). “Experimental Evaluation of Individualized Treatment Rules”,

Author

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School mili@hbs.edu, https://www.michaellz.com/;

Examples

T = c(1,0,1,0,1,0,1,0)
That = matrix(c(0,1,1,0,0,1,1,0,1,0,0,1,1,0,0,1), nrow = 8, ncol = 2)
Y = c(4,5,0,2,4,1,-4,3)
ind = c(rep(1,4),rep(2,4))
pavlist <- PAVcv(T, That, Y, ind)
pavlist$pav
#> [1] -0.125
pavlist$sd
#> [1] 1.278834