Composite change point estimation in bent line quantile regression model for longitudinal data / Menna Tullah Safwat Shalaby ; Supervised Ahmed Mahmoud Gad

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

The obvious feature of longitudinal studies is that the observations of the same subject are correlated over time. Consequently, this leads to having a complicated covariance structure. Most of the time the regression models assume one parametric form for the whole domain of interest, this might not be the case when a change point exists. Con- sequently, the change point{u2019}s existence needs to be investigated and estimated if it does occur. In some cases of change point, the bent line regression models are used. The re- gression models are models in which the function of the response is piecewise but still continuous in covariates. The assumption of normality of the conditional distribution of the response variable is common between regression models. Despite the fact that this is not always the case in real applications, the response variable might follow any other distribution.Therefore, quantile regression is used to model responses that do not follow the normal distribution. Quantile regression is also robust to outliers, and used to model a certain required quantile of the response variable.It was found that in some applications, the change points tend to be similar across different quantile levels. The composite change point estimator for bent line quan- tile regression gathers information from a range of quantiles to estimate the common change point. To our knowledge, it has not been applied on longitudinal data in quantile regression model.This study aims to extend the composite change point estimator to investigate the existence of change point in a quantile regression model in a longitudinal data setting

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