Quantile Regression

7Quantile Regressions with the Ranks of Numerical Predictors

7.1 Introduction

The quantile-regression having numerical independent variables has been called the semiparametric-quantile-regression (SPQR), because the quantiles of the DV are estimated or predicted using the numerical IV. This chapter presents quantile regression having the ranks of numerical variables as predictors or independent variables, which is called the nonparametric-quantile-regression (NPQR). And special notes and comments are presented for SPQR and NPQR. In fact the NPQRs have been presented in the chapter 2, as the QRs (Quantile-Regressions) having categorical IVs. It is recognized that the equations of all Ordinary-Regression (OR) can directly be used to conducting the Quantile-Regression (QR) analysis. In addition, they also can easily be transformed to the Nonparametric-Quantile-Regressions (NPQRs), by replacing their numerical IVs with their ranks. So we can have a lot of possible NPQRs. However, this chapter present only selected alternative NPQRs, starting with the simplest model based on bivariate numerical variables (X,Y).

7.2 NPQRs Based on a Single Rank Predictor

All QRs of Y on a numerical variable X, based on selected data sets from the previous chapters, can easily be transformed to NPQRs using the ranks of X, which can be generated using the following equation:

(7.1a)

Since Ranks_X ...