A comparison of local constant and local linear regression quantile estimators
Computational Statistics & Data Analysis
On spline estimators and prediction intervals in nonparametric regression
Computational Statistics & Data Analysis
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Bankruptcy prediction models based on multinorm analysis: An alternative to accounting ratios
Knowledge-Based Systems
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Two existing methods, namely, local linear quantile regression and self-organizing map (SOM) are combined. The combination provides a fully operational method for the visualization of the @qth quantile q"@q(x) in the conditional distribution of a dependent variable Y given the value X=x of a vector of many covariates. Quantile regression is used to provide a picture of the effect of x on the distribution of Y covering not only the center of the distribution, but also the upper and lower tails. Since the local linear quantile regression model is nonparametric, the shape of the estimate for q"@q(x) may vary both by values of @q and by values of x. The novelty of the proposed methodology ensues from the capability to track these changes in the regression surface via a two-dimensional SOM component plane representation. The methodology eases the interpretation of the dependence between the @qth quantile and covariates that is captured by the conditional quantile function q"@q(x). Moreover, the methodology reveals the sensitivity of this relationship to changes in x that is captured by the gradient of the conditional quantile function @?q"@q(x). Examples using both simulated and real data are provided to illustrate the methodology.