FEENEY . Extreme Value Theory for Non - Stationary Sequences with Applications to Air Pollution Standards . ( Under the direction of

GREGORY ANTHONY FEENEY. Extreme Value Theory for Non-Stationary Sequences with Applications to Air Pollution Standards. (Under the direction of PRANAB KUMAR SEN and MICHAEL JOSEPH SYMONS.) The theory on extreme values has been extended to accommodate certain non-stationary sequences. Of particular interest are -sequences of daily maximum ozone concentrations which, while exhibiting obvious non-stationarity) have previously been treated as either stationary or independent and identically distributed. We restrict consideration to those non-stationary sequences which can be divided into sub-sequences of independent and identically distributed observations, although we allow for stochastic dependence between the sub-sequences. We then extend the classical extreme value theory to accommodate this dependence structure between the subsequences and determine that, under very reasonable conditions, the extreme values for each subsequence are asymptotically jointly independent. The above result enabled us to obtain expressions for the limiting distribution of the k-th extreme value for the entire sequence of observations, for k fixed. We extended these results to the multi-variate situation and considered the case where the sub-sequence sample size is a random variable. We also determined the joint limiting distribution of the sub-sequence maxima. The above theoretical results were applied to a three-year sequence of daily maximum ozone concentrations. The estimation was conducted under the assumption of two parametric models; the Weibull and log-normal; as well as Cox's proportional hazards model, which provided a partial non-parametric estimate of the parent distribution. ii.