Let X1. . . . Xn be i.i.d Uniform over the interval (θ, θ + 1].Show that X(1)+X(n) )/2- 1/2 is also an unbiased estimator of θ, whereX(1) is the minimum order statistic and X(n) is the maximum order statistic. If X - 1/2 is also an unbiased estimator of θ which of the two estimators would you prefer to use.
Answer:-
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Let X1. . . . Xn be i.i.d Uniform over the interval (θ, θ + 1].Show that X(1)+X(n) )/2- 1/2 is also an unbiased estimator of θ, whereX(1) is the minimum order statistic and X(n) is the maximum order statistic. If X - 1/2 is also an unbiased estimator of θ which of the two estimators would you prefer to use.
Let
,
Put
then
Result:-
If are order statics of ,
then r th order statistic
Therefore
Therefore
If
Put
is an unbaised estimation for
From both of these Statistic will choose the statistic which have minimum variance.
have minimum variance will prefer these estimator.
Plz like it...,
Let X1. . . . Xn be i.i.d Uniform over the interval (θ, θ + 1].Show...
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