The application of standard-sufficient dimension reduction (SDR) methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This requirement has plagued their success in high-dimensional data analysis. We propose a unified regression-type estimation strategy, which replaces the degenerate maximum likelihood covariance matrix with a new covariance estimator called Maximum Entropy Covariance (MEC) estimator at the dimension reduction step to produce accurate solutions. The MEC deals directly with singularity and instability of sample group covariance estimates and addresses loss of covariance information in the high-dimensional SDR applications using Maximum Entropy (ME) principle for the first time. We demonstrate the effectiveness of the proposed MEC-SDR methods using real-life Leukemia cancer and customers' electricity load profiles from smart meter data sets.