Moment-based Misclassification Probability for a Quadratic Classifier of Growth Curves using an Edgeworth-type Expansion

Abstract When classifying an observation using a decision rule, there is always a risk of misclassification. The primary objective of this paper is to calculate the first two moments for the plug-in quadratic classifier applied to growth curves with unknown normal distributions, and to use the moments to estimate the misclassification probability. To approximate the misclassification probability, the derived moments are used in an Edgeworth-type expansion of the density for the quadratic classifier. Simulation results demonstrate that as the distance between the groups increases, the probability of misclassification decreases, highlighting the improved classification accuracy when the groups are more clearly separated. Simulations further show that the Edgeworth-type approximation closely matches the Monte Carlo simulated misclassification probability, and consequently, the true misclassification probability.