Heavy-tailed longitudinal data : An adaptive linear regression approach / Wafaa Ibrahim Mohamed Ibrahim ; Supervised Ahmed Mahmoud Gad

Thesis (M.Sc.) - Cairo University - Faculty of Economics and Political Science - Department of Statistics

Longitudinal studies play a prominent role in many social and economics fields. They are indispensable to the study of change in an outcome over time. Special statistical analysis techniques are needed for longitudinal data to accommodate the potential patterns of correlation and variation that might be combined to produce a complicated covariance structure Most of the estimation methods for longitudinal models are based on multivariate normal distribution assumption. However, in many situations this assumption may be violated, for example if the error distribution is heavy tailed. Hence, a proper estimation method is needed in such situations. The least absolute deviation (LAD) estimator minimizes the absolute deviation errors. The adaptive linear regression estimate (ALR) is a linear combination of ordinary least squares (OLS) and least absolute deviations (LAD) are used in case of heavy-tailed cross-sectional data. In the present thesis the least absolute deviation (LAD) estimator developed to accommodate heavy tailed longitudinal data. Also, the adaptive linear regression estimator (ALR) is coined and applied to heavy tailed longitudinal data. Simulation studies are conducted to evaluate the proposed techniques, in addition to applying modified estimators on a real data set

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