Question

Let X1...Xn ~ iid geo(theta) as usual. The pmf is f(x) = theta(1 - theta)^x and E(x) = (1 - theta)/theta. a. Find the method of moments (MOM) estimator for theta hat for theta. b. Use the weak law of large numbers to get an asymptotic limiting value for X. c. Using results from b, argue that the MOM theta hat is a consistent estimator for the unknown theta. d. Use the central limit theorem to get an asymptotic distribution result involving X bar. e. Using the delta method and results from d, obtain a limiting distribution for the MOM theta hat.

Name: let x1xn iid geotheta as usual the pmf is fx theta1 thetax and ex 1 thetatheta a find the method of moments mom estimator for theta hat for theta b use the weak law of large numbers to get a 05636
Uploaded: 2023-10-17T04:53:59-08:00
Duration: 5 min 30 s
Channel: Madhur L
Description: let x1xn iid geotheta as usual the pmf is fx theta1 thetax and ex 1 thetatheta a find the method of moments mom estimator for theta hat for theta b use the weak law of large numbers to get a 05636

          Let X1...Xn ~ iid geo(theta) as usual. The pmf is f(x) = theta(1 - theta)^x and E(x) = (1 - theta)/theta.

a. Find the method of moments (MOM) estimator for theta hat for theta.
b. Use the weak law of large numbers to get an asymptotic limiting value for X.
c. Using results from b, argue that the MOM theta hat is a consistent estimator for the unknown theta.
d. Use the central limit theorem to get an asymptotic distribution result involving X bar.
e. Using the delta method and results from d, obtain a limiting distribution for the MOM theta hat.

Added by Carol M.

Question

Please give Ace some feedback