Maximum likelihood estimators for record-value data with a linear trend are quite sensitive to misspecification of the error distribution. Indeed, incorrect choice of that distribution can lead to inconsistent estimation of the intercept parameter and produce estimators of slope that do not enjoy the asymptotic convergence rate prescribed by the information matrix. These properties and the importance of linearly trended records lead us to suggest a distribution-free approach to inference. We show that the slope and intercept parameters and the entire error distribution can be estimated consistently, and that bootstrap methods are available. The latter may be employed to estimate the variance of estimators of slope, intercept and error distributions. The case of trends that increase faster than linearly is also considered, but is shown to be relatively uninteresting in the sense that the natural estimators have rather predictable properties.
"On distribution-free inference for record-value data with trend." Ann. Statist. 24 (6) 2655 - 2678, December 1996. https://doi.org/10.1214/aos/1032181174