We test the stress shadow hypothesis for large earthquake interactions by examining the relationship between two large earthquakes that occurred in the Mojave Desert of southern California, the 1992 M_w 7.3 Landers and 1999 M_w 7.1 Hector Mine earthquakes. We want to determine if the 1999 Hector Mine earthquake occurred at a location where the Coulomb stress was increased (earthquake advance, stress trigger) or decreased (earthquake delay, stress shadow) by the previous large earthquake. Using four models of the Landers rupture and a range of possible hypocentral planes for the Hector Mine earthquake, we discover that most scenarios yield a Landers-induced relaxation (stress shadow) on the Hector Mine hypocentral plane. Although this result would seem to weigh against the stress shadow hypothesis, the results become considerably more uncertain when the effects of a nearby Landers aftershock, the 1992 M_L 5.4 Pisgah earthquake, are taken into account. We calculate the combined static Coulomb stress changes due to the Landers and Pisgah earthquakes to range from -0.3 to +0.3 MPa (- 3 to +3 bars) at the possible Hector Mine hypocenters, depending on choice of rupture model and hypocenter. These varied results imply that the Hector Mine earthquake does not provide a good test of the stress shadow hypothesis for large earthquake interactions. We use a simple approach, that of static dislocations in an elastic half-space, yet we still obtain a wide range of both negative and positive Coulomb stress changes. Our findings serve as a caution that more complex models purporting to explain the triggering or shadowing relationship between the 1992 Landers and 1999 Hector Mine earthquakes need to also consider the parametric and geometric uncertainties raised here.