Nonparametric Regression Estimation for Nonlinear Systems: A Case Study of Sigmoidal Growths

Sigmoidal growths are well approximated by the non-linear sigmoidal growth models including Richards (1959) Morgan et al (1975), Davies and Ku (1977) and Muller et al (2006) among many others. This article deals with the comparison of the nonparametric regression with the non-linear regression models in order to locate the better approximation for sigmoidal growths. To unwind the standard assumptions, nonparametric regression estimation is used for data analysis, which enables us to look at the data more flexibly, uncovering structure in the data that might missed otherwise. To consider noisy data, observed at certain time or design points, an effort has been made to approximate the relationships without defining the parametric functional form, and to use the function that bears the ability to deal the situation with mild assumptions. The assumptions of smoothness and simplicity are made to make up for usual assumptions of regression models. Kernel estimation and k-nearest neighbor estimation (Hardle, 1990; Takezawa, 2006) is used and the analysis shows the evidence in favor of nonparametric regression estimation (knearest neighbor estimation) with the comparison of non-linear sigmoidal growth models.