A Search for Arrival Direction Clustering in the HiRes-I Monocular Data above $10^{19.5}$ eV

In the past few years, small scale anisotropy has become a primary focus in the search for source of Ultra-High Energy Cosmic Rays (UHECRs). The Akeno Giant Air Shower Array (AGASA) has reported the presence of clusters of event arrival directions in their highest energy data set. The High Resolution Fly's Eye (HiRes) has accumulated an exposure in one of its monocular eyes at energies above $10^{19.5}$ eV comparable to that of AGASA. However, monocular events observed with an air fluorescence detector are characterized by highly asymmetric angular resolution. A method is developed for measuring autocorrelation with asymmetric angular resolution. It is concluded that HiRes-I observations are consistent with no autocorrelation and that the sensitivity to clustering of the HiRes-I detector is comparable to that of the reported AGASA data set. However, because a measure of autocorrelation makes no assumption of the underlying astrophysical mechanism that results in clustering phenomena, we cannot claim that the HiRes monocular analysis and the AGASA analysis are inconsistent beyond a specified confidence level.