Thread: Consistent Estimators and Consistency in Mean Square

1. Re: Consistent Estimators and Consistency in Mean Square

Was referring to this part:

2. Re: Consistent Estimators and Consistency in Mean Square

I know what you were referring to. It's just silly to care about that. You know if epsilon is greater than n if epsilon is greater than n. The thing is that it probably isn't - but that doesn't matter because as n gets large the bottom part goes to 0.

3. Re: Consistent Estimators and Consistency in Mean Square

Yes that is not crucial. But I just wonder how do you calculate the CDF for a given probability mass function of a discrete random variable?

4. Re: Consistent Estimators and Consistency in Mean Square

And to find if it's consistent in mean square, I need to show that it's the tends to 0 as n tends to infinity but what is in each case? i.e. How can I work out expectation if I am given probabilities?

5. Re: Consistent Estimators and Consistency in Mean Square

is just a binary discrete random variable from definition. You should not have trouble with finding its moment if you have taken the elementary probability class.

6. Re: Consistent Estimators and Consistency in Mean Square

So I have to use method of moments and find the first moment?

7. Re: Consistent Estimators and Consistency in Mean Square

I do not mean "method of moment". How do you calculate the expectation of a discrete random variable? E.g. Bernoulli random variable?

8. Re: Consistent Estimators and Consistency in Mean Square

Multiply the possible value by it's probability? so in the first case I have and second case

Is this correct? Also if it is, do I need to add them together to find E

9. Re: Consistent Estimators and Consistency in Mean Square

Yes you need to add them together. This is the basic formula for evaluating the expectation for a discrete random variable. I guess the class you are taking right now assume you are very familiar with this.

10. Re: Consistent Estimators and Consistency in Mean Square

And to find the variance of the estimator?

11. Re: Consistent Estimators and Consistency in Mean Square

Sorry it is really difficult to help you out if you do not know how to compute expectation and variance. Maybe you need to revise your year 1 course first.

http://en.wikipedia.org/wiki/Varianc...andom_variable

For me I will directly calculate and show that it will not converge to 0.

12. Re: Consistent Estimators and Consistency in Mean Square

Originally Posted by BGM
Sorry it is really difficult to help you out if you do not know how to compute expectation and variance. Maybe you need to revise your year 1 course first.
I second this.