Suppose n = Y max is to be used as an estimator for the parameter

Suppose θˆ_n = Y_max is to be used as an estimator for the parameter θ in the uniform pdf, f_Y (y; θ) = 1/θ, 0 ≤ y ≤ θ. Show that θˆ_n is squared-error consistent (see Question 5.7.4).

Data in Question 5.7.4

An estimator θˆ n is said to be squared-error consistent for θ if  

(a) Show that any squared-error consistent θˆ_n is asymptotically unbiased (see Question 5.4.15).

(b) Show that any squared-error consistent θˆ_n is consistent in the sense of Definition 5.7.1.

Transcribed Image Text:

lim E[(Ôn – 0)?] =0 n→∞