How does inclusion of the measurement error in the model, as Y i + Δ i = b X i + ε i affect the standard error of least square estimators b ^ of coefficients b?If I obtain a least squares fit from Y i = b X i + ε i and then later want to incorporate Δ, is it possible to modify my standard error of b ^ to obtain the right value?(You can assume that Δ ∼ N ( 0 , σ 2 ).)

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How does inclusion of the measurement error in the model, as      Y    i    +      Δ    i    =  b      X    i    +      ε    i  affect the standard error of least square estimators             b      ^       of coefficients   b?If I obtain a least squares fit from       Y    i    =  b      X    i    +      ε    i   and then later want to incorporate   Δ, is it possible to modify my standard error of             b      ^       to obtain the right value?(You can assume that   Δ  ∼      N    (  0  ,      σ    2    ).)

furniranizq · Accepted Answer

You can move       Δ          i       to the right-hand side and write      Y          i        =  b      X          i        +  (      ε          i        −      Δ          i        )As long as       Δ          i       is independent and identically distributed (i.i.d) and uncorrelated with       X          i      , the OLS estimate of the   b will be BLUE, that is, the estimate of   b will be unbiased. So you don&#039;t have to modify the standard error of             b      ^      .This is a case of Measurement Error in the Dependent Variable and it is not a problem because of the above explanation. While your estimator isn&#039;t biased you will still lose efficiency as you&#039;ll have more noise on the left-hand side.On the other hand, if it was Measurement Error in the Independent Variable, then your estimator will be biased.

How does inclusion of the measurement error in the model, as Y i </msub> + &

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