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Let X (to) = (W, Y), where W: 9 > W C Rd and Y : R > Y C R. We shall assume that
Let X (to) = (W, Y), where W: 9 > W C Rd and Y : R > Y C R. We shall assume that (Q,.F,P) is a measure space and that (W x Y, B (W) (3: 3 (Y)) is endowed with the probability measure P X. We wish to t the regression model Yeat(W)=a+sTW, where 6 = (11,13) E T C Rd\". Using IID data (Xi-Lew, where each X; = (were) is identical in image measure to X = (W, Y), we wish to estimate the property 6.: = arg min E [39 (W; Ylla is ':s' where s(wiy) = It: a TwI is taken to be the ill-norm loss. (a) Construct an MM algorithm for computing 1 - 6\" = arg min Z 651' \"'1 11:1 naaTm 3 based on (Xiliqnj' (Hint: Use the fact that |a| = ((12, and that a. ri \\/E is a concave function.) Comment on any potential numerical problems, in practice, that may arise when implementing the MM algorithm that you have constructed
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