Consider a sample of size n=8 from the Uniform(θ,θ+4) distribution where θ>0.
Consider two estimators of θ:
T1=X¯ T2=5X¯
(where X¯ denotes the sample mean). By comparing the corresponding MSEs, establish whether T1 is better than T2 to estimate θ.
I wanted to ask you an opinion about this exercise. I cannot understand .
Ok, I know that for compute MSE for T1 for example,
E((T1−θ)^2)=Var(T1−θ)+E2(T1−θ)
=Var(T1)+E2(T1−θ)
Hence it suffices to compute Var(T1) and E(T1−θ)
To compute Var(T1):
Var(T1)=Var(∑Xi/8)
To evaluate the term above, assume Xi
are i.i.d from Uniform(θ,θ+4).
Similarly,
E(T1−θ)=E(∑Xi/8)−θ
After you compute the two MSE value, I choice the one with smaller mean square error.
I don't undetstand how evaluate and what values can assume the term Xi from Uniform(θ,θ+4) for compute my MSE. Can you help me?
Consider two estimators of θ:
T1=X¯ T2=5X¯
(where X¯ denotes the sample mean). By comparing the corresponding MSEs, establish whether T1 is better than T2 to estimate θ.
I wanted to ask you an opinion about this exercise. I cannot understand .
Ok, I know that for compute MSE for T1 for example,
E((T1−θ)^2)=Var(T1−θ)+E2(T1−θ)
=Var(T1)+E2(T1−θ)
Hence it suffices to compute Var(T1) and E(T1−θ)
To compute Var(T1):
Var(T1)=Var(∑Xi/8)
To evaluate the term above, assume Xi
are i.i.d from Uniform(θ,θ+4).
Similarly,
E(T1−θ)=E(∑Xi/8)−θ
After you compute the two MSE value, I choice the one with smaller mean square error.
I don't undetstand how evaluate and what values can assume the term Xi from Uniform(θ,θ+4) for compute my MSE. Can you help me?