# Statistics Estimator Consistency

1. Feb 13, 2010

1) Distribution is a uniform distribution on the interval (Ө, Ө+1)
Show that Ө1 is a consistent estimator of Ө. Ө1=Ῡ -.5
Show that Ө2 is a consistent estimator of Ө. Ө2=Yn – (n/(n+1)).

2) I think the distribution for this one is a uniform distribution on the interval (0, Ө) but I am not 100% sure.
Let Y1, Y2, …, Yn denote a random sample of size n from a power family distribution. Then the method in Section 6.7 imply that Yn=max(Y1, Y2, …, Yn ) has the distribution function of:
0, y<0
Fn(y)= (y/ Ө)^(αn) , 0 ≤ y ≤ Ө
1, y> Ө

Show that Yn is a consistent estimator of Ө.

Last edited: Feb 13, 2010
2. Feb 13, 2010