Estimation of Error Variance in Genomic Selection for Ultrahigh Dimensional Data

Abstract

Estimation of error variance in the case of genomic selection is a necessary step to measure the accuracy of the genomic selection model. For genomic selection, whole-genome high-density marker data is used where the number of markers is always larger than the sample size. This makes it difficult to estimate the error variance because the ordinary least square estimation technique cannot be used in the case of datasets where the number of parameters is greater than the number of individuals (i.e., p > n). In this article, two existing methods, viz. Refitted Cross Validation (RCV) and kfold-RCV, were suggested for such cases. Moreover, by considering the limitations of the above methods, two new methods, viz. Bootstrap-RCV and Ensemble method, have been proposed. Furthermore, an R package “varEst” has been developed, which contains four different functions to implement these error variance estimation methods in the case of Least Absolute Shrinkage and Selection Operator (LASSO), Least Squares Regression (LSR) and Sparse Additive Models (SpAM). The performances of the algorithms have been evaluated using simulated and real datasets.

Application of Regularized Meshless Method with Error Estimation Technique for Water–Wave Scattering by Multiple Cylinders

“…As the number of markers is typically greater than the sample size in genomic selection, the conventional ordinary least squares estimation technique may be insufficient for accurate modeling. Guha Majumdar et al [10] proposed the Bootstrap-RCV and Ensemble method to handle ultrahigh-dimensional data. In the realm of statistical research, where error estimation has seen limited exploration, our work stands as a pioneering endeavor in effectively integrating error estimation techniques with numerical methods.…”