Adzhar Rambli

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.

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.

Multivariate statistical analysis for identifying water quality and hydrogeochemical evolution of shallow groundwater in Quaternary deposits in the Lower Kelantan River Basin, Malaysian Peninsula

A long-term hydrogeochemical data set is used in this study to evaluate the water quality and hydrogeochemical evolution of shallow groundwater in a Quaternary deposit. A multivariate statistical method, hierarchical cluster analysis (HCA), is applied to overcome the problem of a large number of data points in the integration, interpretation and representation of the results. HCA is applied to a subgroup of the hydrogeochemical data set to evaluate their usefulness to classify the groundwater bodies. This subgroup consists of 27 groundwater wells and 15 variables [pH, total dissolved solids, electrical conductivity (EC), Na+, Ca2+, Mg2+, K, HCO3−, Cl−, SO42−, Fe, Mn, NH4, NO3− and SiO2]. Only 12 chemical variables were used for the analysis. Four clusters have been identified: C1–C4, with two main prevalent facies, Na–HCO3 and Ca–HCO3. The hydrogeochemical evolution of shallow groundwater is governed by the processes of precipitation, weathering, dissolution and ion exchange.

A New Discordancy Test in Circular Data Using Spacings Theory

In this article, we propose a new test of discordancy based on spacing theory in circular data. The test should provide a good alternative to existing tests of discordancy for detecting single or well-separated multiple outliers. On top of that, the new method can be generalized to identify a patch of outliers in data. The percentage points are calculated and the performance is examined. We first investigate the performance of the test for detecting a single outlier and show that the new test performs well compared to other known tests. We then show that the generalized test works well in detecting a patch of outliers in the data. As an illustration, a practical example based on an eye dataset obtained from a glaucoma clinic at the University of Malaya Medical Center, Malaysia is presented.

Outlier detection in a new half-circular distribution

In this paper, we use a discordancy test based on spacing theory to detect outlier in a half-circular data. Up to now, numerous discordancy tests have been proposed to detect outlier in circular distributions which are defined in [0,2π). However, some circular data lie within just half of this range. Therefore, first we introduce a new half-circular distribution developed using the inverse stereographic projection technique on a gamma distributed variable. Then, we develop a new discordancy test to detect single or multiple outliers in the half-circular data based on the spacing theory. We show the practical value of the test by applying it to an eye data set obtained from a glaucoma clinic at the University of Malaya Medical Centre, Malaysia.

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.