Leverage values are being used in regression diagnostics as measures of influential observations in the $X$-space. Detection of high leverage values is crucial because of their responsibility for misleading conclusion about the fitting of a regression model, causing multicollinearity problems, masking and/or swamping of outliers, etc. Much work has been done on the identification of single high leverage points and it is generally believed that the problem of detection of a single high leverage point has been largely resolved. But there is no general agreement among the statisticians about the detection of multiple high leverage points. When a group of high leverage points is present in a data set, mainly because of the masking and/or swamping effects the commonly used diagnostic methods fail to identify them correctly. On the other hand, the robust alternative methods can identify the high leverage points correctly but they have a tendency to identify too many low leverage points to be points of high leverages which is not also desired. An attempt has been made to make a compromise between these two approaches. We propose an adaptive method where the suspected high leverage points are identified by robust methods and then the low leverage points (if any) are put back into the estimation data set after diagnostic checking. The usefulness of our newly proposed method for the detection of multiple high leverage points is studied by some well-known data sets and Monte Carlo simulations.diagnostic-robust generalized potentials, group deletion, high leverage points, masking, robust Mahalanobis distance, minimum volume ellipsoid, Monte Carlo simulation,
The population of many countries might undergo dramatic changes in the coming decades due to continuous increases in life expectancy. The sustained reduction in mortality rates and its systematic underestimation has been attracting the significant interest of researchers in recent years because of its potential impact on population size and structure, social security systems, and (from an actuarial perspective) the life insurance and pensions industry worldwide. Among all projection methods, the Lee-Carter method has been widely accepted by the actuarial community. This paper explores the use of the Lee-Carter method to forecast the mortality rates for Malaysian population. The index of the level of mortality for each gender, and the shape and sensitivity coefficients for 18 age groups were obtained through the Lee-Carter method. The Singular Values Decomposition (SVD) is used to forecast the general index for the time period that goes from 2011 to 2030. Since the model involves nonlinear equations that are explicitly difficult to solve, the Matrix Laboratory Version 7.0 (MATLAB 7.0) software will be used in the study. The empirical data sets of Malaysia population for the period of 1981-2010 and for both genders will be considered.
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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