The effect of high leverage points on the logistic ridge regression estimator having multicollinearity AIP Conf.Abstract. In the presence of multicollinearity and multiple outliers, statistical inference of linear regression model using ordinary least squares (OLS) estimators would be severely affected and produces misleading results. To overcome this, many approaches have been investigated. These include robust methods which were reported to be less sensitive to the presence of outliers. In addition, ridge regression technique was employed to tackle multicollinearity problem. In order to mitigate both problems, a combination of ridge regression and robust methods was discussed in this study. The superiority of this approach was examined when simultaneous presence of multicollinearity and multiple outliers occurred in multiple linear regression. This study aimed to look at the performance of several well-known robust estimators; M, MM, RIDGE and robust ridge regression estimators, namely Weighted Ridge M-estimator (WRM), Weighted Ridge MM (WRMM), Ridge MM (RMM), in such a situation. Results of the study showed that in the presence of simultaneous multicollinearity and multiple outliers (in both x and y-direction), the RMM and RIDGE are more or less similar in terms of superiority over the other estimators, regardless of the number of observation, level of collinearity and percentage of outliers used. However, when outliers occurred in only single direction (y-direction), the WRMM estimator is the most superior among the robust ridge regression estimators, by producing the least variance. In conclusion, the robust ridge regression is the best alternative as compared to robust and conventional least squares estimators when dealing with simultaneous presence of multicollinearity and outliers.
In the literature, various nonlinear time series data was shown to exist. As a result, studies on nonlinear models have been carried out. One of them is bilinear model. Further, there is a possibility that outliers may exist in the data. In this article, the possibility of an outlier appear in a special case of bilinear model, BL(1,1,1,1) is investigated. An outlier detection procedure is proposed.
The original Lee-Carter model uses a singular value decomposition approach that assumes constant variance over all ages in estimating the model parameters which falls into a Least Squares framework. Researchers then pointed out that the Lee-Carter model can be treated as a state space model. As a result, several well-established state space modeling techniques were proposed for performing the model parameter estimation, forecasting as well as smoothing. This article investigates a possibility of setting up the state-space representation of the Lee-Carter model with heterogeneous variance assumption over all the age groups in forecasting age-specific death rates (ASDR). The proposed approach was then evaluated by comparing its performance with the Lee-Carter model and Lee-Carter state space model with constant variance assumes over all ages. The parameters of the Lee-Carter state space were estimated by maximum likelihood estimation (MLE) through an expectation-maximization (EM) algorithm. The proposed model was then applied to Malaysian mortality data (from years 1980 to 2011) that split according to gender. Model performance was measured using root mean square error (RMSE) and mean absolute percentage error (MAPE). The results revealed that the LeeCarter state space model with heterogeneous variance is the best model in forecasting Malaysian mortality.
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