Mixing
Ols estimator with the errors following a bernoulli distribution
$begingroup$
I am having trouble understanding how i should approach the following problem:
Given 𝑦𝑖 = 𝛼 + 𝛽𝑥𝑖 + 𝜀𝑖 𝑖 = 1, … , N with 𝜀𝑖 𝑖 = 1,2 … , N being a succession of IID Bernoulli variables with Pr({𝜀𝑖 = 1}) = 1 , Pr({𝜀𝑖 = 0}) = 1 − P
0 < 𝑝 < 1 (p is a known parameter).
Find the OLS estimators for 𝛼̂ e $widehat{𝛽}$.
From this thread, it would appear that the given residuals are missing the mean=0 and costant variance requirements for the ols to be BLUE.
What would the estimated $widehat{Y}$ function look like? Would the 𝜀𝑖 term disappear as usual?
statistics least-squares linear-regression estimation-theory
asked Jan 13 at 22:53
TroubledEconomistTroubledEconomist
12
$endgroup$
add a comment |
$begingroup$
I am having trouble understanding how i should approach the following problem:
Given 𝑦𝑖 = 𝛼 + 𝛽𝑥𝑖 + 𝜀𝑖 𝑖 = 1, … , N with 𝜀𝑖 𝑖 = 1,2 … , N being a succession of IID Bernoulli variables with Pr({𝜀𝑖 = 1}) = 1 , Pr({𝜀𝑖 = 0}) = 1 − P
0 < 𝑝 < 1 (p is a known parameter).
Find the OLS estimators for 𝛼̂ e $widehat{𝛽}$.
From this thread, it would appear that the given residuals are missing the mean=0 and costant variance requirements for the ols to be BLUE.
What would the estimated $widehat{Y}$ function look like? Would the 𝜀𝑖 term disappear as usual?
statistics least-squares linear-regression estimation-theory
asked Jan 13 at 22:53
TroubledEconomistTroubledEconomist
12
$endgroup$
add a comment |
$begingroup$
I am having trouble understanding how i should approach the following problem:
Given 𝑦𝑖 = 𝛼 + 𝛽𝑥𝑖 + 𝜀𝑖 𝑖 = 1, … , N with 𝜀𝑖 𝑖 = 1,2 … , N being a succession of IID Bernoulli variables with Pr({𝜀𝑖 = 1}) = 1 , Pr({𝜀𝑖 = 0}) = 1 − P
0 < 𝑝 < 1 (p is a known parameter).
Find the OLS estimators for 𝛼̂ e $widehat{𝛽}$.
From this thread, it would appear that the given residuals are missing the mean=0 and costant variance requirements for the ols to be BLUE.
What would the estimated $widehat{Y}$ function look like? Would the 𝜀𝑖 term disappear as usual?
statistics least-squares linear-regression estimation-theory
asked Jan 13 at 22:53
TroubledEconomistTroubledEconomist
12
$endgroup$
I am having trouble understanding how i should approach the following problem:
Given 𝑦𝑖 = 𝛼 + 𝛽𝑥𝑖 + 𝜀𝑖 𝑖 = 1, … , N with 𝜀𝑖 𝑖 = 1,2 … , N being a succession of IID Bernoulli variables with Pr({𝜀𝑖 = 1}) = 1 , Pr({𝜀𝑖 = 0}) = 1 − P
0 < 𝑝 < 1 (p is a known parameter).
Find the OLS estimators for 𝛼̂ e $widehat{𝛽}$.
From this thread, it would appear that the given residuals are missing the mean=0 and costant variance requirements for the ols to be BLUE.
What would the estimated $widehat{Y}$ function look like? Would the 𝜀𝑖 term disappear as usual?
statistics least-squares linear-regression estimation-theory
statistics least-squares linear-regression estimation-theory
asked Jan 13 at 22:53
TroubledEconomistTroubledEconomist
12
asked Jan 13 at 22:53
TroubledEconomistTroubledEconomist
12
edited Jan 14 at 20:31
TroubledEconomist
asked Jan 13 at 22:53
TroubledEconomistTroubledEconomist
12
asked Jan 13 at 22:53
TroubledEconomistTroubledEconomist
12
asked Jan 13 at 22:53
TroubledEconomistTroubledEconomist
12
12
add a comment |
add a comment |
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