Statistical Inference Of Parametric Varying Coefficients Regional Quantile Regression

It is common knowledge that research on statistical inference in heteroscedastical regression models has always been a problem attracting a lot of attention in the field of statistical analysis.We consider a class of linear heteroscedastic regression models which can be transformed into parametric varying coefficients regional quantile regression,and propose estimation and test methods based on weighted composite quantile regression to solve the problem of parameter estimation and hypothesis test in the linear heteroscedastic regression model(i.e.parametric varying coefficients regional quantile regression model).The weighted estimation method of the proposed regional quantile model not only has the same efficiency of the composite quantile regression method,but also is simpler than the previous estimation methods.At the same time,the parametric estimators follow the normal distribution asymptotically in the regional quantile model.In order to test the hypothesis of the parameters in the model and better evaluate the test effect,we propose the likelihood ratio statistic and a series of local alternative hypotheses.Considering that the asymptotic distributions of the likelihood ratio statistic under the null hypothesis and local alternatives are too complex and difficult to estimate,we use the random weighted estimation method to construct the random weighted statistic and directly obtain the critical region of the hypothesis test,which can still work well under the local alternative hypotheses.Under the null hypothesis and local alternatives,both the likelihood ratio statistic and the random weighted statistic converge to the same asymptotic distribution and asymptotically follow several linear combinations of(1).This conclusion also shows the rationality of the random weighted resampling method used in the hypothesis test.We evaluate the performance of the proposed methods through numerical simulation.The extensive simulation results show that the proposed estimation and test methods perform well under the limited samples.Meanwhile,we also apply the proposed methods to analyse the overseas study data.