Nonparametric Regression Using Clusters

We present a fundamentally unique method of nonparametric regression using clusters and test it against classically established methods. We compare two nonlinear regression estimation packages called ‘NNS', Viole (NNS: nonlinear nonparametric statistics, 2016), and ‘np', Hayfield and Racine (J Stat Softw 27(5):1–32, 2008), with the help of a simulation using deterministic (DT) and stochastic (ST) regressor models. We find the respective coefficients of determination (R2)(R2) are close for DT models, while finding an advantage to NNS in ST and large sample cases. Regression coefficients are sometimes regarded as approximations to partial derivatives, especially in social sciences. Then, NNS alone has the ability to compute a range of partials evaluated at points within the sample and also out-of-sample. Thus NNS can provide a viable alternative to kernel based nonparametric regressions without using bandwidths for smoothing