"Statistical Tools to Analyze Data Representing a Sample of Curves." Ann. An application to visually evoked brain potentials illustrates the approach. The asymptotic bias and variance of the estimators are derived. They are defined mathematically, their properties are discussed, and possible estimators are proposed. The method requires the introduction of new statistical objects. Pointwise averaging of the synchronized curves then leads to an average curve which represents the common structure with average dynamics and average intensity. Our approach consists in synchronizing the individual curves before determining the average or any further statistics. Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Due to shifts, structure is smeared or might even disappear. For example, the cross-sectional average usually does not reflect an average pattern. Differences in dynamics complicate the analysis of samples of curves. In particular, typical peaks are shifted from individual to individual. This is useful when the data-set has numbers that are not too far from each other. On the other hand, individual realizations of the typical shape show different dynamics and intensity. Some of the important ones are: Central Tendency: Mean, Median, Mode Mean is the summation of all the numbers in a dataset divided by the total number of values. Such samples of curves often possess the following features: There is a typical structural pattern common to all curves of the sample. The paper is concerned with data representing a sample of smooth curves which can be considered as independent realizations of an underlying biological (chemical, $\ldots$) process.
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