Local polynomial bi-responses multi-predictors nonparametric regression for predicting the maturity of mango (Gadung Klonal 21): a theoretical discussion and simulation

Abstract

Determination of mango maturity level can be solved by non-destructive analysis to support one of the SDGs, sustainable production. It is a single example with two responses and several predictors. They created a regression model to handle problems with bi-responses multi-predictors, particularly for local polynomial estimators. This research aims to theoretically build a nonparametric regression model estimate using a local polynomial bi-response multi-predictor. The model can be used to predict the parameters of mango maturity, including the sweetness and acidity of mango. We create the algorithm and R code to show the performance of a bi-response multi-predictor local polynomial estimator based on simulation of three functions data, including trigonometric, exponential, and polynomial functions. The simulation proved that determining the optimal bandwidth based on the generalized cross-validation criterion is the most critical stage in the estimation process. If the bandwidth is too large, the estimation plot will too smooth, and vice versa.  The optimal bandwidth gives the best estimation with the mean square error (MSE) and mean absolute percentage error (MAPE) values less than MSE and MAPE values of non-optimal bandwidth.