Question: For a fixed type of &-corruption we define the maximum bias b(&; X, T) = sup | T(X' ) - T(X) I, where the supremum

 For a fixed type of &-corruption we define the maximum biasb(&; X, T) = sup | T(X' ) - T(X) I, wherethe supremum is taken over all &-corrupted samples X'. The breakdown point

s* is defined as X , if * *(X, T) = infle| b(&; X, T) = 0).exclusively with &-contamination: adjoin m arbitrary valuesY = (y1, . . ., ym) to the sample. The corrupted

For a fixed type of &-corruption we define the maximum bias b(&; X, T) = sup | T(X' ) - T(X) I, where the supremum is taken over all &-corrupted samples X'. The breakdown point s* is defined as X , if * *(X, T) = infle | b(&; X, T) = 0).exclusively with &-contamination: adjoin m arbitrary values Y = (y1, . . ., ym) to the sample. The corrupted sample X' = X U Y then has size n + m and contains a fraction & = m/(n + m) of bad values.Let us assume the e-contamination model (see Huber's paper in week5 folder; in Rd we define the maximum bias as sup | T(x') - T(x) |/2 over all e-contamination). Suppose that 21, . . . , an E R and x = (X1, . ..,n). Show that the estimator T(x) := arg minterd Cilli- t 2 has breakdown point equal to -. Moreover, for any e

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