{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# ps1 - X ∼ N μ x Σ what is the distribution of AX b...

This preview shows page 1. Sign up to view the full content.

1. For a and x both p × 1 vectors, show by example that a 0 x x = a . 2. For A a p × p matrix and x a p × 1 vector, show by example that x 0 Ax x = A + A 0 . 3. Prove that the split sample estimator used to illustrate the Gauss-Markov theorem is unbi- ased. 4. Calculate the OLS estimates of the Nerlove model using Octave and GRETL, and provide printouts of the results. Interpret the results. 5. Do an analysis of whether or not there are influential observations for OLS estimation of the Nerlove model. Discuss. 6. Using GRETL, examine the residuals after OLS estimation and tell me whether or not you believe that the assumption of independent identically distributed normal errors is war- ranted. No need to do formal tests, just look at the plots. Print out any that you think are relevant, and interpret them as carefully and well as you are able to. 7. For a random vector
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: X ∼ N ( μ x , Σ ) , what is the distribution of AX + b , where A and b are conformable matrices of contants? 8. For a random vector X ∼ N ( μ x , Σ ) , what is the distribution of ( X-μ x ) Σ-1 ( X-μ x ) ? 9. Using Octave, write a little program that veri²es that Tr ( AB ) = Tr ( BA ) for A and B con-formable matrices of random numbers. Note: there is an Octave function trace. Note that checking equality using the Octave operation ” == ” will indicate that they are not equal (though in fact they are). Why is that? 10. For the model with a constant and a single regressor, y t = β 1 + β 2 x t + e t , which satis²es the classical assumptions, prove that the variance of the OLS estimator declines to zero as the sample size increases. 1...
View Full 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