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Background and Objective: The existence of outliers in any type of data influences the efficiency of an estimator. Few methods for detecting outliers in a simple circular regression model have been proposed in the study but it suspected that they are not very successful in the presence of multiple outliers in a data set. This study aimed to investigate new statistic to identify multiple outliers in the response variable in a simple circular regression model. Materials and Methods: The proposed statistic is based on calculating robust circular distance between circular residuals and circular location parameter. The performance of the proposed statistic is evaluated by the proportion of detected outliers and the rate of masking and swamping. The simulation study is applied for different sample sizes at 10 and 20% ratios of contamination. Results: The results from simulated data showed that the proposed statistic has the highest proportion of outliers and the lowest rate of masking comparing with some existing methods. Conclusion: The proposed statistic is very successful in detecting outliers with negligible amount of masking and swamping rates.
This study investigates the Unreplicated Linear Functional
Relationship (ULFR) model where the measurement error term, δ, is introduced.
The coefficient of determination (COD) of ULFR, denoted by
is proposed and it properties are investigated. When the introduction of δ
increases significantly the COD, we say that the causation factor has been incorporated
into the independent variable. Present result on the Malaysian road accident
data illustrates the causal relationship between the socio-biological factors
and road accident may be explained.
The relationship between readings on two instruments may be represented by a linear functional relationship with errors of observation in both variables. This study describes a method of fitting the relationship between the two circular variables and the replicate observations are available. Maximum likelihood estimates are used and it is shown that the closed-form expression for the estimators are not available and the estimates may be obtained iteratively by choosing a suitable initial value. The model is illustrated with an application to the analysis of the wave and wind direction data recorded by two different instruments and assuming the pseudo-replicates based on time have been obtained from this unreplicated circular data.
Researchers interest to develop methods of robust estimation. These methods can be used when the data have outliers or not satisfy the condition of classical methods. However, few researchers suggest robust estimation of circular data. In this study, we propose robust estimation of circular variance and mean resultant length. The proposed robust estimation depends on extending trimmed procedure by find robust formula for trimming. Simulation results and practical example show that the proposed procedure for the circular variance and mean resultant length are better than classical methods for different ratios of outliers.
is proposed and it properties are investigated. When the introduction of δ
increases significantly the COD, we say that the causation factor has been incorporated
into the independent variable. Present result on the Malaysian road accident
data illustrates the causal relationship between the socio-biological factors
and road accident may be explained.