Some outlier problems in a circular regression model / Safwati binti Ibrahim

Ibrahim, Safwati (2013) Some outlier problems in a circular regression model / Safwati binti Ibrahim. PhD thesis, University of Malaya.

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Abstract

This study looks at three problems related to the JS circular regression model with five objectives in mind. The first two objectives are concerned with the problem of outliers in the model. The first is the investigation of the robustness of the JS circular regression estimation method in the presence of outliers in the data set. The second is the use of three numerical tests based on row deletion approach to detect possible outliers in the JS circular regression model. The first test considered is a modified version of the COVRATIO statistic by utilizing the covariance matrix of residuals of the JS circular regression model. The other tests are based on the difference mean circular error statistics using cosine and sine functions. For each test, the generation of cut-off points and the power of performance are presented via simulation. In general, the three numerical tests perform well in detecting outliers in JS circular regression model. The next two objectives look at the development of a new generalized JS circular regression model. The third looks at extending the JS circular regression model to include more than one circular explanatory variable. The general formulation of the generalized JS circular regression model and the estimation of the regression parameters using the least squares method are presented. The performance of the estimation method is investigated via simulation and is generally good. The fourth looks at the problem of multicollinearity in the generalized model. A new modified procedure to detect the presence of multicollinearity based on the variance inflation factor is proposed to suit the nature of the generalized JS circular regression model. If the multicollinearity does exist, we use the idea of the ridge regression analysis to find the parameter estimates of the model. The proposed procedure works well when implemented on simulated and real data sets. The last objective is to develop a new functional relationship model framework by using the JS circular regression model in the setup. Here, we assume both the circular dependent and explanatory circular variables are subject to errors. The parameter estimates may be obtained numerically using iterative procedure on the maximum likelihood estimators. Due to the complexity of the estimators, the standard errors of the estimates are obtained using bootstrap method. For illustration, three real circular data sets are considered, namely, wind direction data set, eye data set with two variables and another multivariate eye data set with four variables.

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