#### Jackknife Method

The jackknife method of variance estimation deletes one PSU at a time from the full sample to create replicates. The total number of replicates R 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.

##### Without Stratification

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 jth member of the ith PSU as . If the ith PSU is included in the rth replicate ( ), then the corresponding replicate weight for the jth member of the ith PSU is defined as ##### With Stratification

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 rth 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 jth member of the ith PSU as . If the ith PSU is included in the rth replicate ( ), then the corresponding replicate weight for the jth member of the ith 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 rth replicate by using replicate weights. PROC SURVEYREG estimates the covariance matrix of by with RH degrees of freedom, where R is the number of replicates and H is the number of strata, or R–1 when there is no stratification.