Kernel Estimation of Rate Function for Recurrent Event Data

Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.

EFFECT OF ELECTRICAL DISCHARGE PATTERN ON SPARK IGNITED FLAME KERNEL DEVELOPMENT

Fuel-lean combustion and exhaust gas recirculation (EGR) in spark ignition engines improve engine efficiency and reduce emission. However, flame initiation becomes more difficult in lean and dilute fuel-air mixture with traditional spark discharge. This research proposal will first provide an intensive review on topics related to spark ignition including properties of electrical discharge, flame kernel behavior and spark ignition modeling and simulation. Focus will be laid on electrical discharge pattern effect as it is showing prospect in extending ignition limits in SI engines. An experimental setup has been built with an optically accessible constant volume combustion vessel. Multiple imaging techniques as well as spectroscopy will be applied. By varying spark discharge patterns, preliminary test results are available on consequent flame kernel development. In addition to experimental investigation of spark plasma and flame kernel development, spark ignition modeling with detailed description of plasma channel is also proposed for this study.