Maximum entropy quantile regression with unknown quantile

Abstract

© 2017 by the Mathematical Association of Thailand. All rights reserved. Selecting quantile level in quantile regression model has been problematic for some researchers. Thus, this paper extends the analysis of quantile regression model by regarding its quantile level as an unknown parameter, as it can improve the prediction accuracy by estimating an appropriate quantile parameter for regression predictors. We develop a primal generalized entropy estimation to obtain the estimates of coefficients and quantile parameter. Monte Carlo simulations for quantile regression models with unknown quantile show that the primal GME estimator outperforms other alternatives like least squares and maximum likelihood estimators when the true quantile parameter is assumed to deviate from median. Finally, our model is applied to study the effect of oil price on stock index to examine the performance of the model in real data analysis.