Browsing by Author "Arumairajan, S."
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Item Modified Ridge Type Estimator in Multiple Linear Regression Model(Uva Wellassa University of Sri Lanka, 2019-02) Bahirathan, Y.; Arumairajan, S.Instead of using the Ordinary Least Square Estimator (OLSE), the biased estimators are considered in the multiple linear regression model in the presence of multicollinearity. Some of these are Ridge Estimator (RE), Liu Estimator (LE) and Modified Almost Unbiased Liu Estimator (MAULE). An alternative method for solving the multicollinearity problem is to incorporate the prior information which is available in the form of exact restrictions with sample information. The Restricted Least Square Estimator (RLSE) is proposed by using sample and exact prior information. In the literature, the Restricted Liu Estimator (RLE) is proposed by replacing RLSE instead of OLSE in the LE. Since the combination of two different estimators might inherit the advantages of both estimators, we propose the new estimator named as New Ridge Type Estimator by combining MAULE and RLSE. The stochastic properties of the proposed estimator are obtained. Moreover, the performance of the proposed estimator over the OLSE, RE, MAULE and RLSE in terms of the Scalar Mean Squared Error criterion is investigated by performing a Monte Carlo simulation with the different degrees of collinearity. Furthermore, numerical example is used to evaluate its performance. Based on the simulation study, it has been noticed that the proposed estimator is superior to other existing estimator for some values of shrinkage parameter and different degrees of collinearity. Similarly, it is examined that the proposed estimator is superior to OLSE. According to the numerical example, it can be concluded that the proposed estimator is superior to some other existing estimator for some values of shrinkage parameter. Finally, it can be concluded that proposed estimator is meaningful in practice for the multicollinearity data.Item A New Stochastic Restricted Two Parameter Estimator in Multiple Linear Regression Model(Uva Wellassa University of Sri Lanka, 2021) Kayathiri, S.; Arumairajan, S.Instead of using the Ordinary Least Square Estimator (OLSE) to estimate the regression coefficients, the biased estimators are proposed in the multiple linear regression to overcome the multicollinearity among the predictor variables. An alternative technique to solve the multicollinearity problem is to consider parameter estimation with some restrictions on the unknown parameters, which may be exact or stochastic restrictions. In this research, we propose a biased estimator, namely new stochastic restricted two parameter estimator (NSRTPE) in a multiple linear regression model to tackle the multicollinearity problem when the stochastic restrictions are available. The proposed estimator over the ordinary least square estimator (OLSE), ridge estimator (RE), Liu estimator (LE), almost unbiased Liu estimator (AULE), modified new two parameter estimator (MNTPE), mixed estimator (ME), stochastic restricted Liu estimator (SRLE) are compared in the scalar mean square error (SMSE) sense through a simulation study by considering different levels of multicollinearity and different values of shrinkage parameters (k and d) selected within the interval 0 to 1. From the simulation study, it can be noticed that the proposed estimator performs well than existing estimators when the value of d is large. Furthermore, it can be observed that the proposed estimator is always superior to MNTPE. Finally, it could be concluded that the proposed estimator is meaningful in practice. Keywords: Multiple linear regression; Multicollinearity; Stochastic restriction; New stochastic restricted two parameter estimator; Scalar Mean square errorItem Statistical Modeling of Reselling Price of Suzuki Model Used Car in Colombo District(Uva Wellassa University of Sri Lanka, 2020) Herath, H.M.C.M.; Arumairajan, S.Car reselling is a timely, very popular heading in Sri Lanka and a large number of cars are resold daily. A lot of people are in the practice of reselling their car every time based on different reasons. Many different factors affect the reselling price of used cars. This study aimed to identify the factors that influence the reselling price of used Suzuki cars in Colombo, Sri Lanka, and to find the best multiple linear regression model. For this study, the 90 reselling prices of Suzuki used cars in Colombo district were collected from January 2019 to March 2019. In this study, Mileage of the car in km, Age of the car in years, Model of the car (Swift, Alto, Wagon-R, A-star, and Spacia), Color of the car (Light, Dark) and Number of past owners of the car were considered as independent variables. In this research, a multiple linear regression model has been used to identify the factors that affect the reselling price of the car. Furthermore, the forward selection, backward elimination, and stepwise regression methods have been used to find the best multiple linear regression model. According to the final results of this study, the principal factors that affect the reselling price of used Suzuki cars in Colombo district were mileage of the car, age of the car, the model of the car, and the number of past owners of the car. Finally, the model obtained in this study will be useful for both buyers and sellers. Keywords: Reselling price, Colombo, Used car, Suzuki car, Multiple linear regressionItem Time Series Modelling of Monthly Rainfall in Kilinochchi District, Sri Lanka(Uva Wellassa University of Sri Lanka, 2019-02) Kirisanth, S.; Varathan, N.; Arumairajan, S.The amount of rainfall received over an area is an important factor in assessing availability of water to meet various demands for agriculture, industry and irrigation. Kilinochchi is one of districts in Sri Lanka and many people in Kilinochchi district are below the poverty line and mainly depend on the agriculture for their daily life. Rainfall is the main source of watering for agriculture in Kilinochchi. Forecasting rainfall in Kilinochchi district plays an important role in the planning and management of agriculture scheme and management of water resource systems. Therefore, it is essential to develop a time series model to analyze the amount of rainfall in Kilinochchi district. The main goal of this study is to find a suitable Auto Regressive Integrated Moving Average (ARIMA) model to the monthly rainfall data of Kilinochchi district. In this study, the monthly rainfall of Kilinochchi district under three different stations such as Iranamadu, Akkarayankulam, Kariyalanagapaduwan is modelled by using Box-Jenkins’ time series approach. The monthly rainfall data under three different stations in Kilinochchi district was obtained from the department of meteorology, Sri Lanka during the period of January, 1986 to December, 2015. Further, three statistical criteria such as Akaike information criteria, Bayesian information criteria, mean squared error were used in order to select best the time series model. Through the modelling, it was found that Seasonal Auto Regressive Integrated Moving Average: SARIMA (0,1,1) (0,1,3)12 is the best fitting model for all three stations in Kilinochchi district. Moreover, the adequacy of the fitted best model has been tested using Ljung- Box chi-squared statistic. The identified best model can be used to forecast the monthly rainfall of Kilinochchi district in near future.