The occurrence of spikes during an electroencephalogram is a basic feature of Benign Epilepsy of Childhood (BREC). In this thesis we analyze several problems related to the structure of such spikes. The currently used mathematical model describing the spike assumes that all the inter-spike variations are due to background activity. We show that non-negligible additional variability is present during the spike and propose a slightly richer model which takes such variability into account. In particular we conclude that background noise may not be used to assess the precision of the estimates of the signal. The technique of spike averaging is presently used to obtain more precise estimates of the signal. By comparing averaging with trimmed mean, median and the "lowess" smoother, we find no discrepancies indicating the presence of skewness or long tails in the underlying distribution of the data and conclude that spike averaging is an adequate method for estimating the deterministic part of the spike. Next, three automated procedures for the detection of the peak of the spike are compared to the existing method, which is based on a visual analysis of the EEG tracing. None of the alternative methods is found to be superior, but the methodology developed for this problem is rather general and could be applied to other similar comparisons. Finally we address the question of whether "atypical" BREC patients, who are characterized by having other neurological abnormalities besides seizures, have a spike structure different from that of the "typical" patients. The non parametric method of "classification trees" is discussed and then applied to find whether certain features of the spike can discriminate between typical and atypical patients. The location and amplitude of the spike are found to provide a satisfactory classification rule, suggesting that the two groups may be affected by different types of epilepsy. We have used, throughout the thesis, simple methods which do not require strong assumptions. In particular we have tried to avoid assumptions of normality and linearity and to rely mostly on non parametric methods. / Science, Faculty of / Statistics, Department of / Graduate