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Description:
Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters are estimated by least squares. This paper analyzes forward regression in high-dimensional sparse linear models. Probabilistic bounds for prediction error norm and number of selected covariates are proved. The analysis in this paper gives sharp rates and does not require ß-min or irrepresentability conditions.