PROC QUANTSELECT supports a variety of fit statistics that you can specify as criteria for the CHOOSE= , SELECT= , and STOP= methodoptions in the MODEL statement.
The following fit statistics are available for single quantile effect selection:
applies the Akaike’s information criterion (Akaike 1981; Darlington 1968; Judge et al. 1985).
applies the corrected Akaike’s information criterion (Hurvich and Tsai 1989).
applies the Schwarz Bayesian information criterion (Schwarz 1978; Judge et al. 1985).
specifies the significance level of a statistic used to assess an effect’s contribution to the fit when it is added to or removed from a model. LR1 specifies likelihood ratio Type I, and LR2 specifies the likelihood ratio Type II. By default, the LR1 statistic is applied.
applies the adjusted quantile regression R statistic.
applies the average check loss for the validation data.
Table 96.11 provides formulas and definitions for these fit statistics.
Table 96.11: Formulas and Definitions for Model Fit Summary Statistics for Single Quantile Effect Selection
Statistic 
Definition or Formula 

n 
Number of observations 
p 
Number of parameters including the intercept 

Residual for the ith observation; 

Total sum of check losses; 

Total sum of check losses for interceptonly model if intercept is a forcedin effect, otherwise for emptymodel. 

Average check loss; 

Counterpart of linear regression Rsquare for quantile regression; 

Adjusted R1; 

Akaike’s information criterion; 

Corrected Akaike’s information criterion; 

Schwarz Bayesian information criterion; 
The following statistics are available for quantile process effect selection:
specifies Akaike’s information criterion (Akaike 1981; Darlington 1968; Judge et al. 1985).
specifies the corrected Akaike’s information criterion (Hurvich and Tsai 1989).
specifies Schwarz Bayesian information criterion (Schwarz 1978; Judge et al. 1985).
specifies the adjusted quantile regression R statistic.
specifies average check loss for the validation data.
Table 96.12 provides formulas and definitions for the fit statistics.
Table 96.12: Formulas and Definitions for Model Fit Summary Statistics for Quantile Process Effect Selection
Statistic 
Definition or Formula 

D 
Integral of total sum of check losses; 

Integral of total sum of check losses for interceptonly model or emptymodel if the NOINT option is used; 

Integral of average check loss; 

Counterpart of linear regression Rsquare for quantile process regression; 

Adjusted R1; 

Akaike’s information criterion; 

Corrected Akaike’s information criterion; 

Schwarz Bayesian information criterion; 