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Title:   A Rank-Based Method for Signal Detection in Noisy Time Series

Trend estimates from scattered data are ubiquitous in a broad constellation of disciplines. Arguably the single most common tool for such purposes is the least squares method, which dates back to Carl Friedrich Gauss. So ingrained is this approach that one takes it as an article of faith that, e.g., the least squares output is naturally the "best" estimate of the slope (& intercept). But "best" here means simply the smallest mean squared error. In this lecture we broaden the scope of "best" by exploring the implications of a new rank-based method for trend estimates. This calls into question whether least square estimates really are the most accurate and appropriate characterization of sample variability, realization by realization. A timely application to be covered is the analysis of climate temperature records for evidence of global warming. The rank-based approach especially excels for datasets with extreme events, of which precipitation is one obvious example. Some suggestions for its treatment are presented.