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# (b) ﻿Consider minimising the following penalized sum of squared errors.12( – )2+ (| |)over  , ﻿where   ﻿is the real line and   ﻿is a non-negative tuning

(b) ﻿Consider minimising the following penalized sum of squared errors.12( – )2+ (| |)over  , ﻿where   ﻿is the real line and   ﻿is a non-negative tuning parameter.i. ﻿For  (| |)= 2 2, ﻿show that (1) ﻿is widehat( )= 1+ .[4 ﻿marks]ii. ﻿Take )≠(0, ﻿where  (*) ﻿denotes an indicator function, which is one if the statement in (*) ﻿is true and 0 ﻿otherwise. Show that (1) ﻿is )>( .[5 ﻿marks]

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