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Keywords: Sufficient Dimension Reduction, Maximum Entropy, Smoothed and Hybridized Covariance Estimators, Maximum Entropy Covariance (MEC) Estimator, Information Complexity
In this paper, a new sufficient dimension reduction (SDR) method that contains full information on the entire features in high and low-dimensional data sets is proposed. A new cost-economy unified estimation strategy in regression- and classification-type formulations of SDR methods is presented. The procedure utilised the maximum entropy covariance hybridization and maximal covariance complexity based shrinkage estimation to produce sparse and accurate solutions. The novel contribution here include the hybridization of the newly proposed maximum entropy covariance (MEC) estimator by Olorede and Yahya (2019) with existing smoothed covariance estimators (SCEs) to data-adaptively generate shrunken estimate of the inverse MEC estimator. To our knowledge, utilization of SCEs and Hybridized Smoothed Maximum Entropy Covariance Estimator (HSMEC) in SDR formulation has not been presented in the literature. Our method can be applied to most of the existing SDR methods such as sliced inverse regression, sliced average variance estimation and principal hessian directions. We demonstrated the utility, versatility and effectiveness of the proposed method with electricity clients’ smart meter billing and consumption profiles data and all the results obtained showed that the proposed method is quite efficient with high predictive performance.