Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Consider a r.s. {X_1, X_2, ... , X_n} with size n > 1 from a uniform distribution over [0, ], where 0 <

Consider a r.s. {X_1, X_2, ... , X_n} with size n > 1 from a uniform distribution over [0, ], where 0 < <. Find an order statistic(s) with the smallest variance. Please justify your answer.

More explanation of this question: Following the usual way, we use data {X_1, X-2, ..., X_n} to make our estimation for the parameter theta. To find an order statistic(s), we reorder the known data to {X_(1), X_(2), ..., X_(n)}. Using this kind of data to find statistic(s) is goal of this question. Also, don't forget to prove the variance of the found statistic(s) is the smallest. Variance(T({X_(1), X_(2), ..., X_(n)}) <= Variance(T{X_1, X-2, ..., X_n}) , where Variance(T{X_1, X-2, ..., X_n}) means random statistic(s) for theta. (Here, T( ) means statistics)

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Cambridge IGCSE And O Level Additional Mathematics

Authors: Val Hanrahan, Jeanette Powell

1st Edition

1510421645, 978-1510421646

More Books

Students also viewed these Mathematics questions