Estimation (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 9 - 13 of 14

Describe in Detail

Obtain the sufficient statistics for the following distribution.

(i)

(ii)

Describe in Detail

The observations

3.9, 2.4, 1.8, 3.5, 2.4, 2.7, 2.5, 2.1, 3.0, 3.6, 3.6, 1.8, 2.0, 4.0, 1.5

are a random sample from a rectangular population with pdf

Estimate the parameters by the method of moments.

Describe in Detail

Stating the regularity conditions, give the Cramer-Rao lower bound for the variance of an unbiased estimator of a parameter. Give an example, each, of a situation where the regularity conditions (i) does not hold (ii) holds

Describe in Detail

Explain how the Rao-Blackwell theorem helps one to find a uniformly minimum variance unbiased estimator (UMVUE) of an unknown parameter. What is the relevance of the Lehman-Scheffe theorem in this scenario? If X ₁, X ₂, …, X _n are Bin (1, p) variates, find the UMVUE of p.

Describe in Detail

Let X ₁, X ₂, …, X _n be a random sample from the probability distribution with density

= 0; otherwise

where 0 < θ < ∞. Show that is a minimum variance bound estimator and has variance .