Abstract
The present paper deals with nonlinear, non-monotonic data regression. This paper introduces an efficient algorithm to perform data transformation from non-monotonic to monotonic to be paired with a statistical bivariate regression method. The proposed algorithm is applied to a number of synthetic and real-world non-monotonic data sets to test its effectiveness. The proposed novel non-isotonic regression algorithm is also applied to a collection of data about strontium isotope stratigraphy and compared to a LOWESS regression tool.
Highlights
Every experiment or phenomenological study produces a set of data that, in a large number of instances, is monotonic
As it may be readily observed, the line output of the statistical regression method discussed in the present work agrees pretty well with the ‘Min LOWESS’ inference, except perhaps for a point around 220 Ma where statistical regression seems to adhere more closely to the data than the LOWESS prediction, for the interval 230–250 Ma, where the LOWESS method predicts some spikes, while our method predicts a flatland, and for a point around 400 Ma where the Min LOWESS curve looks pretty smooth, while the curve pertaining to our method presents a spike
The present paper dealt with nonlinear, non-monotonic data regression by isotonic statistical bivariate regression
Summary
Every experiment or phenomenological study produces a set of data that, in a large number of instances, is monotonic (see, for example, the study [1] on nonlinear magnetostatic problems). Regression is a computation application of paramount importance as testified by the research paper [7] that illustrates an application to drowsiness estimation using electroencephalographic data, by the book [8] on statistical methods for engineers and scientists, by [9] that explores an improved power law for nonlinear least-squares fitting, in the papers [10,11,12] that exploit regression analysis in forecasting and prediction, by the research paper [13] that compares a number of linear and non-linear regression methods, in the paper [14] that uses support vector regression for the modeling and synthesis of antenna arrays, and by the contribution [15] that applies kernel Ridge regression to short-term wind speed forecasting. Previous comparative studies [5,16] have clearly shown how statistical regression implemented by look-up tables is much faster in execution than traditional techniques while ensuring the same modeling/regression performance
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