Wavelet-based Non-parametric Estimation of Injury Risk Functions

An injury risk function defines the probability of an injury as a function of certain measurable or known predictors. In this paper, wavelet analysis is employed for the non-parametric estimation of injury risk functions. After a brief introduction of the wavelet theory, the representation of density function by wavelet series is given. A procedure for the estimation of density function is described. The risk function estimation for right-censored data is investigated by introducing hazard rate function and its wavelet estimator. The use of the developed method is illustrated in a case study, where two sets of data are used: simulation data with known distribution and censoring information, and thoracic impact testing data, which are assumed to be right- censored. Comparisons are made between the wavelet-based approach and the empirical Kaplan-Meier non-parametric method.