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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

May 5, 2024

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

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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

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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