The two most important activities in maize breeding are the development of inbred lines with high values of general combining ability (GCA) and specific combining ability (SCA), and the identification of hybrids with high yield potentials. Genomic selection (GS) is a promising genomic tool to perform selection on the untested breeding material based on the genomic estimated breeding values estimated from the genomic prediction (GP). In this study, GP analyses were carried out to estimate the performance of hybrids, GCA, and SCA for grain yield (GY) in three maize line-by-tester trials, where all the material was phenotyped in 10 to 11 multiple-location trials and genotyped with a mid-density molecular marker platform. Results showed that the prediction abilities for the performance of hybrids ranged from 0.59 to 0.81 across all trials in the model including the additive effect of lines and testers. In the model including both additive and non-additive effects, the prediction abilities for the performance of hybrids were improved and ranged from 0.64 to 0.86 across all trials. The prediction abilities of the GCA for GY were low, ranging between − 0.14 and 0.13 across all trials in the model including only inbred lines; the prediction abilities of the GCA for GY were improved and ranged from 0.49 to 0.55 across all trials in the model including both inbred lines and testers, while the prediction abilities of the SCA for GY were negative across all trials. The prediction abilities for GY between testers varied from − 0.66 to 0.82; the performance of hybrids between testers is difficult to predict. GS offers the opportunity to predict the performance of new hybrids and the GCA of new inbred lines based on the molecular marker information, the total breeding cost could be reduced dramatically by phenotyping fewer multiple-location trials.

Genomic prediction (GP) has become a valuable tool for predicting the performance of selection candidates for the next breeding cycle. A vast majority of statistical linear models on which GP is based rely on the assumption of normality of the residuals and therefore on the response variable itself. In this study, we propose to use Bayesian regularized quantile regression (BRQR) in the context of GP; the model has been successfully used in other research areas. We evaluated the prediction ability of the proposed model and compared it with the Bayesian ridge regression (BRR; equivalent to genomic best linear unbiased predictor, GBLUP). In addition, BLUP can be used with pedigree information obtained from the coefficient of coancestry (ABLUP). We have found that the prediction ability of BRQR is comparable to that of BRR and, in some cases, better; it also has the potential to efficiently deal with outliers. A program written in the R statistical package is available as Supplementary material.