The application of jackknife statistics to estimates of the recombination fraction

We develop and evaluate the jackknife statistics [Efron, 1982] for obtaining confidence intervals for the recombination fraction. We consider two cases: (1) a single sibship of size S with phase known parents (one doubly heterozygous and one doubly homozygous) and (2) a sample of 20 nuclear families. We compare the jackknife confidence interval to the -1.00 lod and -0.83 lod intervals. For the first case we compare our intervals with a confidence interval which we develop that has coverage of exactly 95%. For the second case, we do a simulation study and compare the coverage of the intervals and the endpoints of the intervals with the actual 2.5th and 97.5th percentiles. Our results indicate that in case (1) the lod intervals provide closer estimates to the 95% exact interval than does the jackknife approach. However, in case (2), although the lod intervals have better coverage probabilities, the jackknife interval endpoints are closer to the actual percentile points than either of the lod interval endpoints.