Question

0Let X₁, ....., X_n be iid Random variable from a Uniform distribution $(-\theta, \theta)$ with pdf given by$f_x(x|\theta) = \frac{1}{2\theta}*I(-\theta < x < \theta), \theta > 0$ .

(1) Is the 2-dimensional statistics T₁(X) = (X₍₁₎, X_(n)) a complete sufficient statistics? Justify your answer

(2) Is the one-dimensional statistic $T_2(x) = max_i\{|X_i|\}$ a complete sufficient statistic? Justify your answer

Answer 1

(1) solution :

Given data :

2-dimensional statistics T₁(X) = (X₍₁₎

Now we have to justify :

Is the 2-dimensional statistics T₁(X) = (X₍₁₎, X_(n)) a complete sufficient statistics:

Yes, the 2-dimensional statistics T₁(X) = (X₍₁₎, X_(n)) is a complete sufficient statistics.

• The given two dimensional measurement is a finished adequate measurement
• Since we can get the unbiased assessed estimation of the main parameter

(2) solution :

Given data :

one-dimensional statistic  $T_2(x) = max_i\{|X_i|\}$

Now, we have to justify :

Is the one-dimensional statistic $T_2(x) = max_i\{|X_i|\}$ a complete sufficient statistic:

Yes,  the one-dimensional statistic $T_2(x) = max_i\{|X_i|\}$ a complete sufficient statistic

• The given one dimensional measurement is a finished adequate measurement
• Since we can get the unprejudiced assessed estimation of the main parameter .

Note: As per the HOMEWORKLIB RULES, two questions are enough. so i am answered the question 1 and 2 .If you want remaining  question please re upload as another question.

Thank you,