Genomic prediction is now widely recognized as an efficient, cost-effective and theoretically well-founded method for estimating breeding values using molecular markers spread over the whole genome. The prediction problem entails estimating the effects of all genes or chromosomal segments simultaneously and aggregating them to yield the predicted total genomic breeding value. Many potential methods for genomic prediction exist but have widely different relative computational costs, complexity and ease of implementation, with significant repercussions for predictive accuracy. We empirically evaluate the predictive performance of several contending regularization methods, designed to accommodate grouping of markers, using three synthetic traits of known accuracy. Each of the competitor methods was used to estimate predictive accuracy for each of the three quantitative traits. The traits and an associated genome comprising five chromosomes with 10000 biallelic Single Nucleotide Polymorphic (SNP)-marker loci were simulated for the QTL-MAS 2012 workshop. The models were trained on 3000 phenotyped and genotyped individuals and used to predict genomic breeding values for 1020 unphenotyped individuals. Accuracy was expressed as the Pearson correlation between the simulated true and the estimated breeding values. All the methods produced accurate estimates of genomic breeding values. Grouping of markers did not clearly improve accuracy contrary to expectation. Selecting the penalty parameter with replicated 10-fold cross validation often gave better accuracy than using information theoretic criteria. All the regularization methods considered produced satisfactory predictive accuracies for most practical purposes and thus deserve serious consideration in genomic prediction research and practice. Grouping markers did not enhance predictive accuracy for the synthetic data set considered. But other more sophisticated grouping schemes could potentially enhance accuracy. Using cross validation to select the penalty parameters for the methods often yielded more accurate estimates of predictive accuracy than using information theoretic criteria.