The jackknife method of variance estimation deletes one PSU at a time from the full sample to create replicates. The total number of replicates is the same as the total number of PSUs. In each replicate, the sample weights of the remaining PSUs are modified by the jackknife coefficient . The modified weights are called replicate weights.
The jackknife coefficient and replicate weights are described as follows.
If there is no stratification in the sample design (no STRATA statement), the jackknife coefficients are the same for all replicates:
Denote the original weight in the full sample for the th member of the th PSU as . If the th PSU is included in the th replicate (), then the corresponding replicate weight for the th member of the th PSU is defined as
If the sample design involves stratification, each stratum must have at least two PSUs to use the jackknife method.
Let stratum be the stratum from which a PSU is deleted for the th replicate. Stratum is called the donor stratum. Let be the total number of PSUs in the donor stratum . The jackknife coefficients are defined as
Denote the original weight in the full sample for the th member of the th PSU as . If the th PSU is included in the th replicate (), then the corresponding replicate weight for the th member of the th PSU is defined as
You can use the VARMETHOD=JACKKNIFE(OUTJKCOEFS=) method-option to save the jackknife coefficients into a SAS data set and use the VARMETHOD=JACKKNIFE(OUTWEIGHTS=) method-option to save the replicate weights into a SAS data set.
If you provide your own replicate weights with a REPWEIGHTS statement, then you can also provide corresponding jackknife coefficients with the JKCOEFS= option.
Let be the estimated regression coefficients from the full sample for . Let be the estimated regression coefficient obtained from the th replicate by using replicate weights. PROC SURVEYREG estimates the covariance matrix of by
with degrees of freedom, where is the number of replicates and is the number of strata, or when there is no stratification.