Post-selection Inference For Varying Coefficient Quantile Regression Models

Varying coefficient models are generalized from the linear regression model.Because of the variability of its coefficients,it has better flexibility and interpretability than the linear regression models.Compared with the mean regression method,the quantile regression method comprehensively describes each quantile of the response variable.Varying coefficient quantile regression models might as well.Further,varying coefficient models are widely used in many scientific fields and have become the important statistical models.In this thesis,we study the inference post-model selection of varying coefficient quantile regression models.Firstly,the B-spline method is used on the basis expansion of varying coefficients effectively avoiding problems such as “dimensional disaster”.Secondly,based on the variable selection of varying coefficient quantile regression models,we apply the de-biased estimation theory to obtain a de-biased estimator.Then,we derive a consistent Bahadur representation of varying coefficient quantile models based on the de-biased estimators.Under certain conditions,we prove that the consistent Bahadur representation is consistent for any quantile and varying coefficient's parameters.Simultaneously,we prove that it converges to the Brown Bridge process.By this property,we further construct the confidence interval estimators and guarantee its coverage probabilities.Finally,numerical simulation and empirical data analysis prove the limited sample properties of the theory and make it the based theory support.