Use the method described in Exercise 9.26 to show that, if Y (1) = min( Y 1 , Y 2 , . .., Y n ) when Y 1 , Y 2 , … , Y n are independent uniform random variables on the interval (0 , θ ) , then Y (1) is not a consistent estimator for θ . [ Hint: Based on the methods of Section 6.7 , Y (1) has the distribution function F ( 1 ) ( y ) = { 0 , y < 0 , 1 − ( 1 − y / θ ) n , 0 ≤ y ≤ θ , 1 , y > θ . ]
Use the method described in Exercise 9.26 to show that, if Y (1) = min( Y 1 , Y 2 , . .., Y n ) when Y 1 , Y 2 , … , Y n are independent uniform random variables on the interval (0 , θ ) , then Y (1) is not a consistent estimator for θ . [ Hint: Based on the methods of Section 6.7 , Y (1) has the distribution function F ( 1 ) ( y ) = { 0 , y < 0 , 1 − ( 1 − y / θ ) n , 0 ≤ y ≤ θ , 1 , y > θ . ]
Solution Summary: The author proves that Y_(1) is not a consistent estimator of.
Use the method described in Exercise 9.26 to show that, if Y(1) = min(Y1, Y2, . .., Yn) when Y1, Y2, … , Yn are independent uniform random variables on the interval (0, θ) , then Y(1) is not a consistent estimator for θ. [Hint: Based on the methods of Section 6.7 , Y(1) has the distribution function
F
(
1
)
(
y
)
=
{
0
,
y
<
0
,
1
−
(
1
−
y
/
θ
)
n
,
0
≤
y
≤
θ
,
1
,
y
>
θ
.
]
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
se 3
Let Y1, Y2,..., Yn denotes a random sample from the uniform distribution on the
interval (0,0 + 1). Let
Ô = Y -2
and 02 =Y(n)-
n+1
%3D
Show that both 6, and 02 are consistent estimators for 0.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.