zeta function

zeta function in sensitivity analysis

Of limited interest to most users, the zeta function plays an internal role in 2-sample and stratified sensitivity analyses. The zeta function is equation (8), page 495, in Rosenbaum and Krieger (1990).

zeta(bigN, n, m, g)

Arguments

• bigN: Total sample size in this stratum.
• n: Treated sample size in this stratum.
• m: The number of 1's in the vector u of unobserved covariates. Here, u has bigN-m 0's followed by m 1's.
• g: The sensitivity parameter $\Gamma$, where $\Gamma \ge 1$.

Returns

The value of the zeta function.

References

Rosenbaum, P. R. and Krieger, A. M. (1990). Sensitivity of two-sampler permutation inferences in observational studies. Journal of the American Statistical Association, 85, 493-498.

Rosenbaum, P. R. (2002). Observational Studies (2nd edition). New York: Springer. Section 4.6.

Author(s)

Paul R. Rosenbaum

Note

The zeta function is called by computep.

Examples

zeta(10,5,6,2)