The Residual Plot for a Non–Linear Regression Model with the Presence of Outliers and Heteroscedastic Errors

Abstract

Regresi teguh adalah sangat berguna bagi menilai kecukupan satu penyesuaian dan mencadangkan penjelmaan yang sesuai. Ini boleh dicapai dalam hanya satu pelaksanaan penganggaran teguh dan bukannya membina satu diagnostik titik terpencil. Dalam kertas ini, prestasi plot reja bagi Penganggar Teguh MM Berpemberat (WMM) dibandingkan dengan plot reja Kuasadua Terkecil Tak Linear (NLLS), Kuasadua Terkecil Tak Linear Teritlak (GNLLS) dan Penganggar Teguh MM. Dari keputusan berangka yang diperoleh, menyatakan bahawa plot reja NLLS dan GNLLS sukar mengenal pasti titik terpencil dan titik pelarasan tinggi. Lagipun, ianya tidak menunjukkan corak impian dalam selang reja [–2.5, 2.5]. Plot reja GNLLS dan WMM menghasilkan corak impian apabila varian ralat adalah heterosedastik dan tiada kekotoran berlaku dalam data set. Plot reja dari MM boleh mengenal pasti titik terpencil tetapi reja dalam selang [–2.5, 2.5] menyatakan bahawa ianya menokok dengan menokoknya tindakbalas penganggar, yang mungkin memerlukan penjelmaan yang sesuai. Plot reja WMM mempamerkan corak impian unggul dengan rejanya yang bertaburan secara rawak di dalam selang [–2.5, 2.5]. Kata kunci: Titik terpencil, regresi teguh, heterosedastik, penganggar MM berpemberat Robust regression is extremely useful in assessing the adequacy of a fit and suggesting appropriate transformations. This can be achieved in a single run by using robust estimation methods instead of constructing outlier diagnostics. In this paper, the performance of the residual plot of the robust Weighted MM estimators (WMM) was compared with the Non–Linear Least Squares (NLLS), Generalized Non–Linear Least Squares (GNLLS), and robust MM residual plots. The results obtained from numerical examples signified that the residual plots from the NLLS and the GNLLS fit can hardly identify outliers and high leverage points. Furthermore, it did not show an ideal pattern in the residuals within [–2.5, 2.5] interval. The GNLLS and the WMM residual plots revealed an ideal pattern when the error variances were heteroscedastic and no contamination occured in the data set. The residual plot from the MM fit can identify outliers but the residuals within the [–2.5, 2.5] interval indicated that the residuals increased with increasing estimate response, which may suggest an appropriate transformation. The WMM residual plot exhibited a pronounced ideal pattern denoted by its residuals, which were randomly distributed within [–2.5, 2.5] interval. Key words: Outliers, robust regression, heteroscedastic, weighted MM estimator