A complex linear regression model

This paper gives a comprehensive discussion on complex regression model by extending the idea of regression model to circular variables. Various aspect have been considered such as the biasness of parameters, error assumptions and model checking. The advantage of this approach is that it allows the use of usual technique available in ordinary linear regression for the regression of circular variables. The quality of the estimates and the feasibility of the approach were illustrated via simulation. The model was then applied to the wave direction data

The Comparison Between Maximum Weighted and Trimmed Likelihood Estimator of The Simple Circular Regression Model

The Maximum Likelihood Estimator (MLE) was used to estimate unknown parameters of the simple circular regression model. However, it is very sensitive to outliers in data set. A robust method to estimate model parameters is proposed

The Comparison Between Maximum Weighted and Trimmed Likelihood Estimator of The Simple Circular Regression Model

The Maximum Likelihood Estimator (MLE) was used to estimate unknown parameters of the simple circular regression model. However, it is very sensitive to outliers in data set. A robust method to estimate model parameters is proposed

Robust detection of outliers in both response and explanatory variables of the simple circular regression model

It is very important to make sure that a statistical data is free from outliers before making any kind of statistical analysis. This is due to the fact that outliers have an unduly affect on the parameter estimates. Circular data which can be used in many scientific fields are not guaranteed to be free from outliers. Often, the relationship between two circular variables is represented by the simple circular regression model. In this respect, outliers might occur in the both response and explanatory variables of the circular model. In circular literature, some researchers show interest to identify outliers only in the response variable. However, to the best of our knowledge, no one has proposed a method which can detect outliers in both the response and explanatory variables of the circular linear model. Thus, in this article, an attempt has been made to propose a new method which can detect outliers in both variables of the simple circular linear model. The proposed method depends on the robust circular distance between the response and the explanatory variables in the model. Results from the simulations and real data example show the merit of our proposed method in detecting outliers in simple circular model

Estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance

In this study, we propose the estimation of the concentration parameter for simultaneous circular functional relationship model. In this case, the variances of the error term are not necessarily equal and the ratio of the concentration parameter λ = is not necessarily 1. The modified Bessel function was expended by using the asymptotic power series and it became a cubic equation of κ. From the cubic equation of κ, the roots were obtained by using the polyroot function in SPlus software. Simulation study was done to study the mean, estimated bias, absolute relative estimated bias, estimated standard error and estimated root mean square error of the estimation of the concentration parameter. From the simulation study, large concentration parameter and sample size show that the estimated concentration parameter has smaller bias. Also, an illustration to a real wind and wave data set is given to show its practical applicability

Finding the best circular distribution for southwesterly monsoon wind direction in Malaysia

In this paper, four types of circular probability distribution were used to evaluate which circular probability distribution gives the best fitting for southwesterly Malaysian wind direction data, namely circular uniform distribution, von Mises distribution, wrapped-normal distribution and wrapped-Cauchy distribution. The four locations chosen were Alor Setar, Langkawi, Melaka and Senai. Two performance indicators or goodness of fit tests which are mean circular distance and chord length were used to test which distribution give the best fitting

Robust trimmed mean direction to estimate circular location parameter in the presence of outliers

Mean direction is a good measure to estimate circular location parameter in univariate circular data. However, it is bias and cause misleading when the circular data has some outliers, especially with increasing ratio of outliers. Trimmed mean is one of robust method to estimate location parameter. Therefore in this study, it is focused to find a robust formula for trimming the circular data. This proposed method is compared with mean direction, median direction and M estimator for clean and contaminated data. Results of simulation study and real data prove that trimmed mean direction is very successful and the best among them

Adjusting outliers in univariate circular data

Circular data analysis is a particular branch of statistics that sits somewhere between the analysis of linear data and the analysis of spherical data. Circular data are used in many scientific fields. The efficiency of the statistical methods that are applied depends on the accuracy of the data in the study. However, circular data may have outliers that cannot be deleted. If this is the case, we have two ways to avoid the effect of outliers. First, we can apply robust methods for statistical estimations. Second, we can adjust the outliers using the other clean data points in the dataset. In this paper, we focus on adjusting outliers in circular data using the circular distance between the circular data points and the circular mean direction. The proposed procedure is tested by applying it to a simulation study and to real data sets. The results show that the proposed procedure can adjust outliers according to the measures used in the paper

Detection of Outliers in Univariate Circular Data using Robust Circular Distance

A robust statistic to detect single and multi-outliers in univariate circular data is proposed. The performance of the proposed statistic was tested by applying it to a simulation study and to three real data sets, and was demonstrated to be robust

On robust estimation for slope in linear functional relationship model

In this paper, we propose a robust parameter estimation method for the linear functional relationship model. We improved the maximum likelihood estimation using robust estimators and robust correlation coefficients to estimate the slope parameter. The performance of the propose method, MMLE, is compared with the standard maximum likelihood estimation (MLE) and the nonparametric method in terms of mean square error. The results for simulation studies suggested the performance of the MMLE and nonparametric methods gives better estimate than the standard MLE in the presence of outliers. The novelty of the proposed method is that it is not affected by the presence of outliers and is simple to use. To illustrate practical application of the methods, we obtain the estimate of the slope parameter in a study of body-composition techniques for children