Parameter estimation and outlier detection in linear functional relationship model / Adilah Abdul Ghapor

Adilah, Abdul Ghapor (2017) Parameter estimation and outlier detection in linear functional relationship model / Adilah Abdul Ghapor. PhD thesis, University of Malaya.

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Abstract

This research focuses on the parameter estimation, outlier detection and imputation of missing values in a linear functional relationship model (LFRM). This study begins by proposing a robust technique for estimating the slope parameter in LFRM. In particular, the focus is on the non-parametric estimation of the slope parameter and the robustness of this technique is compared with the maximum likelihood estimation and the Al-Nasser and Ebrahem (2005) method. Results of the simulation study suggest that the proposed method performs well in the presence of a small, as well as high, percentage of outliers. Next, this study focuses on outlier detection in LFRM. The COVRATIO statistic is proposed to identify a single outlier in LFRM and a simulation study is performed to obtain the cut-off points. The simulation results indicate that the proposed method is suitable to detect a single outlier. As for the multiple outliers, a clustering algorithm is considered and a dendogram to visualise the clustering algorithm is used. Here, a robust stopping rule for the cluster tree base on the median and median absolute deviation (MAD) of the tree heights is proposed. Simulation results show that the proposed method performs well with a small value of masking and swamping, thus implying the suitability of the proposed method. In the final part of the study on the missing value problem in LFRM, the modern imputation techniques, namely the expectation-maximization (EM) algorithm and the expectation-maximization with bootstrapping (EMB) algorithm is proposed. Simulation results show that both methods of imputation are suitable in LFRM, with EMB being superior to EM. The applicability of all the proposed methods is illustrated in real life examples.

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