Search

In survival and reliability studies, hazard-rate function plays an important role. Sudden changes in the hazard function may occur due to treatment effects or maintenance activities. A problem of statistical interest is the estimation of the times of the changes, as well as their sizes. In this note, we review the basic estimation methods for hazard change-point models for complete data. Some related literature is also provided for estimation with incomplete data and hypothesis testing. Keywords: hazard rate; change-point; estimation

Recent developments in analysis methods for event‐related functional magnetic resonance imaging (fMRI) has enabled a wide range of novel experimental designs. As with selective averaging methods used in event‐related potential (ERP) research, these methods allow for the estimation of the average time‐locked response to particular event‐types, even when these events occur in rapid succession and in an arbitrary sequence. Here we present a flexible framework for obtaining efficient and unbiased estimates of event‐related hemodynamic responses, in the presence of realistic temporally correlated (nonwhite) noise. We further present statistical inference methods based upon the estimated responses, using restriction matrices to formulate temporal hypothesis tests about the shape of the evoked responses. The accuracy of the methods is assessed using synthetic noise, actual fMRI noise, and synthetic activation in actual noise. Actual false‐positive rates were compared to nominal false‐positive rates assuming white noise, as well as local and global noise estimates in the estimation procedure (assuming white noise resulted in inappropriate inference, while both global and local estimates corrected false‐positive rates). Furthermore, both local and global noise estimates were found to increase the statistical power of the hypothesis tests, as measured by the receiver operating characteristics (ROC). This approach thus enables appropriate univariate statistical inference with improved statistical power, without requiring a priori assumptions about the shape or timing of the event‐related hemodynamic response. Hum. Brain Mapping 11:249–260, 2000. © 2000 Wiley‐Liss, Inc.