Concepts of can and caun estimators

Question

Question 1:

a) Define MVUE and illustrate a method of getting MVUE.

b) Explain the concepts of sufficiency and minimal sufficiency. Describe how minimal sufficiency is associated to bound completeness.

Question 2:

a) State and prove the Cehmann-Schffe theorem.

b) Obtain the general form of distribution admitting sufficient statistic.

Question 3:

a) Describe the concepts of CAN and CAUN estimators. Describe the construction of CAN estimators which is based on moments.

b) Explain the maximum likelihood method of estimation. Find out an ML estimator for the parameter θ in f (x, θ) = (1 + θ) x^θ, 0 < x < 1, θ > 0 based on a sample of size n.

Question 4:

a) Describe the general method of obtaining confidence limits. Explain the criterion for the selection of a confidence interval from among infinite set of confidence intervals.

b) Define:

• Efficiency
• Consistency

Question 5:
a) Differentiate between non- randomized and randomized construct MP critical region for a random sample from N (M, σ²) with M known but σ² is unknown.

b) Derive the asymptotic distribution of the LR test criterion.