CAREER: Asymptotics of random processes and their applications

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The proposal aims to advance statistical theory for randomprocesses that exhibit features like long-range dependence andnonlinearities, and to educate both statisticians and othersscientists in this new exciting area. Compared to thewell-developed theory under the independence assumption, it isconsiderably more challenging to establish a limit theory forprocesses with such features. The Principal Investigator proposesa powerful martingale based method and studies spectralestimation, empirical processes, nonparametric estimation andother related asymptotic problems for such processes.Processes with long-range dependence and nonlinearities occur invarious fields, including computer networks, communication,finance, geology, hydrology, econometrics and atmospheric scienceamong others. Applications of the research results developed inthe proposal would help test and justify claims made by scientistsin such fields. In particular, the PI develops statisticalmethodology to identify trends in temperature and ozone sequencesand provides statistical reasoning for meteorologists' claims onclimate change patterns.