One assumption in OLS is that E(X,X) is full-rank. In practice, however, the data matrix X'X...

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One assumption in OLS is that E(X,X) is full-rank. In practice, however, the data matrix X'X could be close to noninvertible because of imperfect multicollinearity or sampling noise. Ridge estimator in machine learning proposes a practical solution: Let Y be nx 1 and X be nx k. For model Y = XB + E, assume E(X₁₁) = 0 and all other assumptions hold. Define the ridge estimator as *-((2x.x) + x) (2x.x.). where A is a positive constant and I is the k x k identity matrix. Ridge resolves the nearly- noninvertible issue because it enlarges the diagonal elements in X'X mechanically. Show that Bis consistent for B. = One assumption in OLS is that E(X,X) is full-rank. In practice, however, the data matrix X'X could be close to noninvertible because of imperfect multicollinearity or sampling noise. Ridge estimator in machine learning proposes a practical solution: Let Y be nx 1 and X be nx k. For model Y = XB + E, assume E(X₁₁) = 0 and all other assumptions hold. Define the ridge estimator as *-((2x.x) + x) (2x.x.). where A is a positive constant and I is the k x k identity matrix. Ridge resolves the nearly- noninvertible issue because it enlarges the diagonal elements in X'X mechanically. Show that Bis consistent for B. =

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