Estimation of parameters and outlier detection in replicated linear functional relationship model / Azuraini Mohd Arif

Azuraini , Mohd Arif (2023) Estimation of parameters and outlier detection in replicated linear functional relationship model / Azuraini Mohd Arif. PhD thesis, Universiti Malaya.

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Abstract

The thesis focuses on parameter estimation especially in the presence of outliers, outlier detection and grouping procedures in a linear functional relationship model (LFRM). There are two categories of LFRM: the unreplicated and replicated model. The study starts by modifying the maximum likelihood estimation method in unreplicated LFRM when the ratio of error variances is equal to one. A robust slope estimator namely the modified maximum likelihood estimation method is proposed. Results from simulation studies show that the modified maximum likelihood estimation method is outlier resistant and performs well than the traditional maximum likelihood estimation method. Then, an improvement on the estimation of the parameters by introducing balanced replicated observations in the LFRM when there is no information about the ratio of error variances is proposed. The estimation of parameters using maximum likelihood estimation method along with the variance-covariance matrix using the Fisher Information matrix is derived. Based on the simulation studies, the estimated values of the parameters are found to be unbiased and consistent. Next is the construction of the robust slope estimator using a 20% trimmed mean based on the nonparametric method. The robustness of this method is compared with the maximum likelihood method for replicated LFRM. Simulation results show that the 20% trimmed mean performs well even the datasets have a high number of outliers. The second part of the study focuses on outlier detection in replicated LFRM using COVRATIO statistic. The cut-off points and the performance of the method are obtained from the simulation study. From simulation results, the cut-off points obtained and power of performance is suggested that the COVRATIO statistic can be used to detect a single outlier in replicated LFRM. The last part of the study concentrates on proposing a practical group method in clustering analysis. The motivation is to transform observation that are of unreplicated data to replicated data. Three clustering methods are considered and simulation studies are used to assess the performance of the parameter estimate of replicated LFRM. The benefits of these approach is that it can be done without making an assumption on the ratio of error variances. The applicability of all proposed methods is illustrated in published datasets.

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