Parameter estimation and outlier detection for some types of circular model / Siti Zanariah binti Satari

Satari, Siti Zanariah (2015) Parameter estimation and outlier detection for some types of circular model / Siti Zanariah binti Satari. PhD thesis, University of Malaya.

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Abstract

This study focuses on the parameter estimation and outlier detection for some types of the circular model. We first look at the concentration parameter of von Mises distribution. The von Mises distribution is the most commonly used probability distribution of a circular random variable, and the concentration of a circular data set is measured using the mean resultant length. We propose a new and efficient approximation of the concentration parameter estimates using two approaches, namely, the roots of a polynomial function and minimizing the negative value of the loglikelihood function in this study. Secondly, we consider the construction of confidence interval for the unknown parameter of a type of circular regression model, namely the model by Down and Mardia (2002). The parameters being considered in this study is the error concentration parameter. The confidence interval of the error concentration parameter is not straight forward due to the complexity of getting a closed form and the wrap-around nature of the data. In this study, we propose an alternative method of constructing a confidence interval based from the distribution of the estimated value of error concentration parameter obtained from the Fisher information matrix. Thirdly, a new functional relationship model for circular variables, which is an extended version of a circular regression model as proposed by Down and Mardia (2002), is developed in this study. Both the dependent and independent variables in the model are subjected to errors. We derive the maximum likelihood estimation of parameters as well as the variance-covariance of parameters. Later, we assess the performance of confidence interval for error concentration parameter for the new functional relationship model via simulation study. Lastly, we consider the problem of detecting multiple outliers in circular regression models based on the clustering algorithm. We develop the clustering-based procedure for the predicted and residual values obtained from the Down and Mardia model fit of a circular-circular data set. Here, we introduce a measure of similarity based on the circular distance and obtain a cluster tree using the single linkage clustering algorithm. Then, a stopping rule for the cluster tree based on the mean direction and circular standard deviation of the tree height is proposed. We classify the cluster group that exceeds the stopping rule as potential outliers. Model verification of all method and model proposed in this study are examined using the simulation study. As illustration, applications are displayed using wind and wave circular data sets.

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