Composite Quantile Regression Based On QIF For Partial Linear Model Of Longitudinal Data

Longitudinal data refers to data obtained from repeated observations of the same individual at different times or spaces,so it combines elements of both cross-sectional data and time series data,which can fully reflect the relationship between the data.Partial linear models combine the advantages of both parametric and non-parametric models,which have strong interpretation capabilities and are very flexible.So partial linear models are widely used in longitudinal data modeling.When making statistical inferences on a partially linear model of longitudinal data,when the model's random errors no longer meet the assumptions or the data distribution is abnormal,many existing estimation methods lack robustness and do not consider the intra-group correlations of longitudinal data.Therefore,this paper estimates the model using a compound quantile regression method based on a quadratic inference function.The estimation method combined with quantile regression of multiple quantiles yields more robust estimation results;and the estimation method uses a quadratic inference function to introduce a working correlation matrix,which can effectively deal with the internal correlation of individual longitudinal data.In this paper,the asymptotic normality of the estimate is proved under certain conditions,and a smooth estimation algorithm is further given.Finally,the finite sample nature of the estimate is proved by simulation and applied to an example.