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1. Substitute Eq. (3) under expectation sign and use addiditve property of expectation

1. Substitute Eq. (3) under expectation sign and use addiditve property of expectation. 2. All expectations are equal. (3). 4. Use the results of the first paragraph. 5. Algebraic rearrangements. 6. Used triangle inequality |a + b| ≤ |a| + |b|. 7. (8). (9).

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1. Substitute Eq. (3) under expectation sign and use addiditve property of expectation

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  1. 1. Substitute Eq. (3) under expectation sign and use addiditve property of expectation 2. All expectations are equal (3) 4. Use the results of the first paragraph 5. Algebraic rearrangements 6. Used triangle inequality |a + b| ≤ |a| + |b| 7.

  2. (8) (9) 10. Discrete version of Schwartz inequality below+ Equation (9) and 11. Schwartz inequality: See the next page

  3. 12. 13. Apply definition of kq from paragraph 4 to this expression 14. First expression multiplied by is o(1) and thus, this limit exists because all previous expressions are algebraic transformations. Last limit is finite (see paragraph 6). 15. Consequence of paragraph 5 and See page 5 Because in second Equation (15), the sum does not depend on T, the sum is finite. Here and below C is some constant.

  4. 16. By the Eq. (15) Because kqf(q) does not depend on T, Finite by construction Finite, by paragraph 6 17. The expression is equal to 18. Putting together the results of paragraph 5, expression for the bias from the introduction and the definition of from paragraph 7. we obtain this result.

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