P Set 6 - 1 MGTECON 603 Econometrics I Fall 2009 PROBLEM...

• Notes
• 2

This preview shows pages 1–2. Sign up to view the full content.

1 MGTECON 603, Econometrics I Jules H. van Binsbergen Fall 2009 Stanford GSB PROBLEM SET 6 Due: Monday November 16 th 1. Let X 1 , X 2 , . . . , X N represent a random sample from a Poission distribution with arrival rate λ . (a) Find the maximum likelihood estimator for λ and its asymptotic distribution. (b) Suppose we are interested in the probability of a count of zero, θ = Pr ( X = 0) = exp( - λ ). Find the maximum likelihood estimator for θ and its asymptotic distribution. (c) Show that X i is a sufficient statistic. (d) Find an unbiased estimator for θ . (Hint: define Y as the indicator for the event X = 0. Then E [ Y ] = Pr ( X = 0).) Is this estimator a function of the sufficient statistic? Modify the estimator to make sure it is a function of the sufficient statistic. (e) How does the variance of the unbiased estimator compare to the asymptotic vari- ance of the maximum likelihood estimator? 2. Let X 1 , X 2 , . . . , X N represent a random sample from each of the distributions having the following probability density functions. In each case find the asymptotic variance

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern