Outlier Detections and Robust Estimation Methods for Nonlinear Regression Model Having Autocorrelated and Heteroscedastic Errors

The ordinary Nonlinear Least Squares (NLLS) and the Maximum Likelihood Estimator (MLE) techniques are often used to estimate the parameters of nonlinear models. Unfortunately, many researchers are not aware of the consequences of using such estimators when outliers are present in the data. The prob...

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Main Author:	Riazoshams, Hossein
Format:	Thesis
Language:	English English
Published:	2010
Subjects:	Outliers (Statistics) Regression analysis - Mathematical models. Autocorrelation (Statistics)
Online Access:	http://psasir.upm.edu.my/id/eprint/19681/1/IPM_2010_13.pdf
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id	my-upm-ir.19681
record_format	uketd_dc
spelling	my-upm-ir.196812013-05-27T08:02:50Z Outlier Detections and Robust Estimation Methods for Nonlinear Regression Model Having Autocorrelated and Heteroscedastic Errors 2010-11 Riazoshams, Hossein The ordinary Nonlinear Least Squares (NLLS) and the Maximum Likelihood Estimator (MLE) techniques are often used to estimate the parameters of nonlinear models. Unfortunately, many researchers are not aware of the consequences of using such estimators when outliers are present in the data. The problems get more complex when the assumption of constant error variances or homoscedasticity is violated. To remedy these two problems simultaneously, we proposed a Robust Multistage Estimator (RME). The heterogeneouity of error variances is considered when the variances of residuals follows a parametric functional form of the predictors. Both Nonlinear model function parameters and variance model parameters must be robustified. We have incorporated the MM, the generalized MM and the robustified Chi-Squares Pseudo Likelihood function in the formulation of the RME. The results of the study reveal that the RME is more efficient than the existing methods. The thesis also addresses the problems when the assumptions of the independent error terms are not met. We proposed a new Robust Two Stage (RTS) estimator in this regard. The proposed method is developed by incorporating the generalized MM estimator in the classical two stage estimator. The performance of the RTS is more efficient than other existing methods revealed by having the highest robustness measures. We also proposed two outlier identification measures in nonlinear regression. The Tangent leverage, the NLLS, the M and the MM estimators are incorporated in the formulation of the first outlier identification measures. The formulation of the second measure is based on the differences between the derived robust Jacobian Leverage and Tangent leverage. Both proposed measures are very successful to identify the correct outliers. Finally, we proposed statistics practitioners to use the formal modeling algorithms to get better inferences. We also suggest them to employ appropriate robust methods for further analysis once a correct model has been chosen. The results of the study based on real data signify that the robust estimator is more efficient indicated by lower values of standard errors when compared to the classical estimator Outliers (Statistics) Regression analysis - Mathematical models. Autocorrelation (Statistics) 2010-11 Thesis http://psasir.upm.edu.my/id/eprint/19681/ http://psasir.upm.edu.my/id/eprint/19681/1/IPM_2010_13.pdf application/pdf en public phd doctoral Universiti Putra Malaysia Outliers (Statistics) Regression analysis - Mathematical models. Autocorrelation (Statistics) Institute of Mathematical Research English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Outliers (Statistics) Regression analysis - Mathematical models. Autocorrelation (Statistics)
spellingShingle	Outliers (Statistics) Regression analysis - Mathematical models. Autocorrelation (Statistics) Riazoshams, Hossein Outlier Detections and Robust Estimation Methods for Nonlinear Regression Model Having Autocorrelated and Heteroscedastic Errors
description	The ordinary Nonlinear Least Squares (NLLS) and the Maximum Likelihood Estimator (MLE) techniques are often used to estimate the parameters of nonlinear models. Unfortunately, many researchers are not aware of the consequences of using such estimators when outliers are present in the data. The problems get more complex when the assumption of constant error variances or homoscedasticity is violated. To remedy these two problems simultaneously, we proposed a Robust Multistage Estimator (RME). The heterogeneouity of error variances is considered when the variances of residuals follows a parametric functional form of the predictors. Both Nonlinear model function parameters and variance model parameters must be robustified. We have incorporated the MM, the generalized MM and the robustified Chi-Squares Pseudo Likelihood function in the formulation of the RME. The results of the study reveal that the RME is more efficient than the existing methods. The thesis also addresses the problems when the assumptions of the independent error terms are not met. We proposed a new Robust Two Stage (RTS) estimator in this regard. The proposed method is developed by incorporating the generalized MM estimator in the classical two stage estimator. The performance of the RTS is more efficient than other existing methods revealed by having the highest robustness measures. We also proposed two outlier identification measures in nonlinear regression. The Tangent leverage, the NLLS, the M and the MM estimators are incorporated in the formulation of the first outlier identification measures. The formulation of the second measure is based on the differences between the derived robust Jacobian Leverage and Tangent leverage. Both proposed measures are very successful to identify the correct outliers. Finally, we proposed statistics practitioners to use the formal modeling algorithms to get better inferences. We also suggest them to employ appropriate robust methods for further analysis once a correct model has been chosen. The results of the study based on real data signify that the robust estimator is more efficient indicated by lower values of standard errors when compared to the classical estimator
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Riazoshams, Hossein
author_facet	Riazoshams, Hossein
author_sort	Riazoshams, Hossein
title	Outlier Detections and Robust Estimation Methods for Nonlinear Regression Model Having Autocorrelated and Heteroscedastic Errors
title_short	Outlier Detections and Robust Estimation Methods for Nonlinear Regression Model Having Autocorrelated and Heteroscedastic Errors
title_full	Outlier Detections and Robust Estimation Methods for Nonlinear Regression Model Having Autocorrelated and Heteroscedastic Errors
title_fullStr	Outlier Detections and Robust Estimation Methods for Nonlinear Regression Model Having Autocorrelated and Heteroscedastic Errors
title_full_unstemmed	Outlier Detections and Robust Estimation Methods for Nonlinear Regression Model Having Autocorrelated and Heteroscedastic Errors
title_sort	outlier detections and robust estimation methods for nonlinear regression model having autocorrelated and heteroscedastic errors
granting_institution	Universiti Putra Malaysia
granting_department	Institute of Mathematical Research
publishDate	2010
url	http://psasir.upm.edu.my/id/eprint/19681/1/IPM_2010_13.pdf
_version_	1747811441371512832

Outlier Detections and Robust Estimation Methods for Nonlinear Regression Model Having Autocorrelated and Heteroscedastic Errors

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