Quantile Regression And Variable Selection For Growth Curve Model

In this paper, we mainly study the quantile regression and variable selection of the Growth Curve Model which has the expression of The Growth Curve Model is widely used in biology and it can be transformed into a general linear model through arithmetic. Then we can study it by using some methods which have already been existed.Parameters estimation and variable selection are critical in statistical modeling. In this paper we come to a conclusion by using theoretical analysis and comparative study that compared with OLS,the smallest subset selection and stepwise regression, the Quantile Regression with Adaptive-Lasso method performs much better. We mention that classical OLS has two shortages regardless of some merits in itself. One shortage of OLS is that the error of an estimator is too large leading to the model we get is not precise enough. Another is that OLS can’t eliminate useless variables which may lead to the expression of a model is not good enough. At the same time, the smallest subset selection method and stepwise regression also have shortages.For these shortages, we put forward a new parameters estimation method--Quantile Regression which is proposed by Konenker and Bassett(1978). We also prove that Quantile Regression is more robust than OLS when the distribution is excess kurtosis and heavy tail. Then we introduce the Adaptive-Lasso penalty method. It has oracle property and can shrink the coefficients with small absolute value to zero which realize the aim of variable selection. So we consider to combine quantile regression and the penalty method and get the Quantile Regression with Adaptive-Lasso method.Then we show its oracle property and algorithms derivations. In the end, we proved that this method performs good in parameters estimation and variable selection by numerical modeling.