Abdul Ghapor Hussin

Outlier Detection in a Circular Regression Model Using COVRATIO Statistic

In this article, we model the relationship between two circular variables using the circular regression models, to be called JS circular regression model, which was proposed by Jammalamadaka and Sarma (1993). The model has many interesting properties and is sensitive enough to detect the occurrence of outliers. We focus our attention on the problem of identifying outliers in this model. In particular, we extend the use of the COVRATIO statistic, which has been successfully used in the linear case for the same purpose, to the JS circular regression model via a row deletion approach. Through simulation studies, the cut-off points for the new procedure are obtained and its power of performance is investigated. It is found that the performance improves when the resulting residuals have small variance and when the sample size gets larger. An example of the application of the procedure is presented using a real dataset.

Detection of outliers in simple circular regression models using the mean circular error statistic

The investigation on the identification of outliers in linear regression models can be extended to those for circular regression case. In this paper, we propose a new numerical statistic called mean circular error to identify possible outliers in circular regression models by using a row deletion approach. Through intensive simulation studies, the cut-off points of the statistic are obtained and its power of performance investigated. It is found that the performance improves as the concentration parameter of circular residuals becomes larger or the sample size becomes smaller. As an illustration, the statistic is applied to a wind direction data set.

Statistics for a New Test of Discordance in Circular Data

This article considers the derivation of approximate distributions for two types of statistics that can be used in developing new tests of discordance in circular samples from the von Mises distribution. An alternative test of discordance is proposed based on the circular distance between sample points. The advantage of the test is that it allows users to detect possible outliers in both univariate and bivariate circular data. For illustration, the test is applied to two real circular data sets.

Procedures for outlier detection in circular time series models

It is known that the occurrence of outliers in linear or non-linear time series models may have adverse effects on the modelling and statistical inference of the data. Consequently, extensive research has been conducted on developing outlier detection procedures so that outliers may be properly managed. However, no work has been done on the problem of outliers in circular time series data. This problem is the focus of this paper. The main objective is to develop novel numerical and graphical procedures for detecting these outliers in circular time series data.A number of circular time series models have been proposed including the circular autoregressive model. We extend the iterative outlier detection procedure which has been successfully used in linear time series models to the circular autoregressive model. The proposed procedure shows a good performance when investigated via simulation for the circular autoregressive model of order one. At the same time, several statistical techniques have been used to detect the change of preferred trend in time series data using SLIME and CUSUM plots. While the methods fail to indicate directly the outliers in circular time series data, we use the ideas employed to develop three novel graphical procedures for identifying the outliers. For illustration, we apply the procedures to a particular set of wind direction data. An agreement between the results of the graphical and iterative detection procedures is observed. These procedures could be very useful in improving the modelling and inferential processes for circular time series data.

An Alternative Analysis of Two Circular Variables via Graphical Representation

The relationship between variables is vital in data analysis. The scatter plot, for instance, gives an easy preliminary exploratory analysis for finding relationship between two variables, if any. Statistical method such as correlation and linear relationship are standard tools in most statistical packages. For circular variables that take value on the circumference of a circle, the analysis however is different from those of the Euclidean type variables because circumference is a bounded closed space. Unlike linear variable, standard statistical packages for circular variables are limited. This paper proposes a graphical representation of two circular variables as a preliminary analysis using the MATLAB environment. A plot called Spoke plot is developed to visually display relationship between two circular variables and linear correlation. As an illustration, the Malaysian wind data is used in the analysis. This new type of representation promises an alternative approach in the preliminary analysis of circular data.

A clustering approach to detect multiple outliers in linear functional relationship model for circular data

ABSTRACT Outlier detection has been used extensively in data analysis to detect anomalous observation in data. It has important applications such as in fraud detection and robust analysis, among others. In this paper, we propose a method in detecting multiple outliers in linear functional relationship model for circular variables. Using the residual values of the Caires and Wyatt model, we applied the hierarchical clustering approach. With the use of a tree diagram, we illustrate the detection of outliers graphically. A Monte Carlo simulation study is done to verify the accuracy of the proposed method. Low probability of masking and swamping effects indicate the validity of the proposed approach. Also, the illustrations to two sets of real data are given to show its practical applicability.

Detecting multiple outliers in linear functional relationship model for circular variables using clustering technique

Outlier detection has been used extensively in data analysis to detect anomalous observation in data and has important application in fraud detection and robust analysis. In this paper, we propose a method in detecting multiple outliers for circular variables in linear functional relationship model. Using the residual values of the Caires and Wyatt model, we applied the hierarchical clustering procedure. With the use of tree diagram, we illustrate the graphical approach of the detection of outlier. A simulation study is done to verify the accuracy of the proposed method. Also, an illustration to a real data set is given to show its practical applicability.

Procedure for Detecting Outliers in a Circular Regression Model.

A number of circular regression models have been proposed in the literature. In recent years, there is a strong interest shown on the subject of outlier detection in circular regression. An outlier detection procedure can be developed by defining a new statistic in terms of the circular residuals. In this paper, we propose a new measure which transforms the circular residuals into linear measures using a trigonometric function. We then employ the row deletion approach to identify observations that affect the measure the most, a candidate of outlier. The corresponding cut-off points and the performance of the detection procedure when applied on Down and Mardia’s model are studied via simulations. For illustration, we apply the procedure on circadian data.

A new technique to solve the unidentifiablity problem of linear structural relationship model

Several techniques have been used to solve the unidentifiability problem of linear structural relationship model. Most of them assumed either the error variance σδ2 or σe2 is known or both are known or the ratio of them is known and then can be used to estimate the rest of parameters. In this study, we assume the slope parameter, β is known and then derive the maximum likelihood estimate (MLE) for rest of the parameters. In fact, the slope is estimated separately by a nonparametric method and assumed to be known when the rest of the parameters are estimated by maximum likelihood method. We obtain closed-form estimates of parameters and their variances and covariances. Using a simulation study, we showed that the estimated values of the parameters are unbiased and consistent. Finally, this method is illustrated using real data set.