2014/04/11 by Hong Pi, Pi, Hong, Carsten Peterson +1
Computer Science · Engineering · Mathematics · #Advanced Statistical Methods and Models #Chaotic Dynamics (nlin.CD) #Control Systems and Identification #FOS: Computer and information sciences #FOS: Economics and business #FOS: Physical sciences #Machine Learning (stat.ML) #Neural Networks and Applications #Statistical Finance (q-fin.ST)
paper · pdf · doi:10.48550/arxiv.1404.3219
openalex publication_date 2014/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A method for estimating nonlinear regression errors and their distributions without performing regression is presented. Assuming continuity of the modeling function the variance is given in terms of conditional probabilities extracted from the data. For N data points the computational demand is N2. Comparing the predicted residual errors with those derived from a linear model assumption provides a signal for nonlinearity. The method is successfully illustrated with data generated by the Ikeda and Lorenz maps augmented with noise. As a by-product the embedding dimensions of these maps are also extracted.