Dow Theory’s Peak-and-Trough Analysis Justified

Scale-Invariance Ideas Explain the Empirical Soil-Water Characteristic Curve

“…Which value a should we choose for this modified intermediate dependence: general idea. In our analysis, we can use an observation (made in the 1980s by B. S. Tsirelson [16]) that in many cases, when we reconstruct the signal from the noisy data, and we assume that the resulting signal belongs to a certain class, the reconstructed signal is often an extreme point from this class; see also [11,15]. The paper [16] provided the following geometric explanation to this fact: namely, when we reconstruct a signal from a mixture of a signal and a Gaussian noise, then the maximum likelihood estimation (a traditional statistical technique; see, e.g., [14]) means that we look for a signal which belongs to the (a priori determined) class of signals, and which is the closest -in the sense of the usual Euclidean distance -to the observed signal-plus-noise combination.…”