Bias and variance residuals for machine learning nonlinear simplex regressions

We propose two new residuals that can be used to evaluate the bias and variance of nonlinear simplex regressions for machine learning. Such models are supervised learning tools for problems with high complexity, since they involve nonlinearity, and are used with univariate responses that assume values in the standard unit interval. The residuals we introduce are obtained from Fisher’s iterative scoring algorithm used for estimating the mean and dispersion regression coefficients. A novel feature of the proposed residuals is that they do not require the computation of projection matrices. As is well known, the computation of such matrices can be computationally costly when the sample size is large. We present and discuss three empirical applications, two that use real data and one that is based on a simulated dataset. The results from all three empirical analyses favor the proposed residuals.