Verbetering van die voorspellingsakkuraatheid van regressiemodelle met minimale aannames

Abstract

Die voorspellingsakkuraatheid van 'n regressiemodel maak in 'n groot mate staat op die toepaslikheid van die modelbouer se aannames. Daarbenewens kan die teenwoordigheid van uitskieters ook tot modelle lei wat onbetroubaar en dus minder robuust is. In hierdie artikel word 'n regressiemodel wat op minimale aannames gebaseer is, bestudeer en uitgebrei in 'n poging om voorspellingsakkuraatheid te verbeter. Die voorgestelde uitbreidings sluit uitskieteropsporing in wat op wiskundige programmeringstegnieke gebaseer is, asook 'n gladstrykingstegniek wat gebruik word om die koers van verandering in die rigting van 'n funksie te beheer. Die voorgestelde modelleringstegnieke word dan op vier welbekende datastelle uit die literatuur toegepas om hul voorspellingsakkuraatheid te illustreer en te evalueer. Die resultate toon dat die twee uitbreidings die voorspellingsvermoë van die oorspronklike minimale-aanname-regressiemodel (soos deur die gemiddelde absolute afwyking gemeet) aansienlik verbeter het. Die resultate vergelyk ook gunstig met ander modelle, soos stuksgewyse lineêre regressiemodelle. ABSTRACT: Improving the predictive accuracy of regression models with minimal assumptions The forecasting accuracy of a regression model relies heavily on the applicability of the assumptions that have been made by the model builder. In addition, the presence of outliers may also lead to models that are not reliable and thus less robust. In this paper a regression model based on minimal assumptions is considered and extended in an effort to improve forecasting accuracy. The proposed extensions include outlier detection that is based on mathematical programming techniques and a smoothing technique that is used to control the rate of change in direction of a function. The suggested modelling techniques are then applied to four well-known data sets from the literature to illustrate and evaluate their forecasting accuracy. The results show that the two extensions have significantly improved the prediction capability of the original minimal assumption regression model (as measured by the mean absolute deviation). The results also compare favourably with those of other models, such as piecewise linear regression models.