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a linear model with d = 5 variables and n = 50 observations. Starting from the left, the columns are X, and 0.00000 1.20706 -0.66487 0.46392 0.19746 -0.38526 6.18304 1.05715 -0.50740 0.27952 0.00000 -0.17280 12.48795 0.91734 -0.36985 0.11063 0.00000 0.00000 16.89171 0.82829 -0.28890 0.00000 0.00000 0.00000 33.19002 0.53551 0.00000 0.00000 0.00000 0.00000 0.00000 59.28000 0.00000 0.00000 0.00000 0.00000 report your procedure and the required quantity.

a linear model with d = 5 variables and n = 50 observations. Starting from the left, the columns are X, and 0.00000 1.20706 -0.66487 0.46392 0.19746 -0.38526 6.18304 1.05715 -0.50740 0.27952 0.00000 -0.17280 12.48795 0.91734 -0.36985 0.11063 0.00000 0.00000 16.89171 0.82829 -0.28890 0.00000 0.00000 0.00000 33.19002 0.53551 0.00000 0.00000 0.00000 0.00000 0.00000 59.28000 0.00000 0.00000 0.00000 0.00000 report your procedure and the required quantity.

Question
The following table contains output from a lasso fit to a linear model with d = 5 variables and n = 50 observations. Starting from the left, the columns are X, and B₁,..., B5, i.e. each row has X and the transposed column vector (X). 0.00000 1.20706 -0.66487 0.46392 0.19746 -0.38526 6.18304 1.05715 -0.50740 0.27952 0.00000 -0.17280 12.48795 0.91734 -0.36985 0.11063 0.00000 0.00000 16.89171 0.82829 -0.28890 0.00000 0.00000 0.00000 33.19002 0.53551 0.00000 0.00000 0.00000 0.00000 59.28000 0.00000 0.00000 0.00000 0.00000 0.00000 For each of the required computations below, briefly report your procedure and the required quantity. a) For each row in the table, compute s, the proportion of shrinkage defined as s = s(X) = ||B(A)||₁/ maxx ||B(A)||1- b) Consider X'= 25.040865. Note that X' is the intermediate value between λ = 16.89171 and λ = 33.19002 of the 4th and 5th rows above. Using this value of X', compute and report the shrunk estimator B(x'). c) Give the proportion of shrinkage s(X') for the shrunk estimator (X').
Transcribed Image Text:The following table contains output from a lasso fit to a linear model with d = 5 variables and n = 50 observations. Starting from the left, the columns are X, and B₁,..., B5, i.e. each row has X and the transposed column vector (X). 0.00000 1.20706 -0.66487 0.46392 0.19746 -0.38526 6.18304 1.05715 -0.50740 0.27952 0.00000 -0.17280 12.48795 0.91734 -0.36985 0.11063 0.00000 0.00000 16.89171 0.82829 -0.28890 0.00000 0.00000 0.00000 33.19002 0.53551 0.00000 0.00000 0.00000 0.00000 59.28000 0.00000 0.00000 0.00000 0.00000 0.00000 For each of the required computations below, briefly report your procedure and the required quantity. a) For each row in the table, compute s, the proportion of shrinkage defined as s = s(X) = ||B(A)||₁/ maxx ||B(A)||1- b) Consider X'= 25.040865. Note that X' is the intermediate value between λ = 16.89171 and λ = 33.19002 of the 4th and 5th rows above. Using this value of X', compute and report the shrunk estimator B(x'). c) Give the proportion of shrinkage s(X') for the shrunk estimator (X').
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