Suppose that C is an n n symmetric idempotent matrix with rank r and let a Show that C AA, where A is n r with AA Ir b Show that AV N(0r, Ir) c Show that VCV Xr2 V N(0 In)...

Suppose that C is an n n symmetric idempotent matrix with rank r and let a.

Question:

Suppose that C is an n Ã— n symmetric idempotent matrix with rank r and let

a. Show that C = AA€², where A is n Ã— r with A€²A = Ir.
b. Show that A€²V ~ N(0r, Ir).
c. Show that V€²CV ~ Xr2.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Introduction to Econometrics

ISBN: 978-0133595420

3rd edition

Authors: James H. Stock, Mark W. Watson

Question Posted: Apr 29, 2016 03:38 PM

See More Questions

If A1, A2, , Ak, is an infinite sequence of n Ã n matrices, then the sequence is said to converge to the n Ã n matrix , A if the entries in the ith row and jth column of the sequence...
In this exercise we consider how to generate matrices with specified ranks using MATLAB. (a) In general, if A is an m n matrix with rank r, then r min(m, n). Why? Explain. If the entries of A are...
Let A be a symmetric matrix (that is, A = AT) with distinct eigenvalues Î»1 and Î»2. For such a matrix, if v1 and v2 are eigenvectors belonging to the distinct eigenvalues...
a. An autoregressive model is given by: Yt = 20.58 + 0.046 yt-1 + 0.01Yt-2 where Y, = sales of a product. Explain the meaning of the terms in this autoregressive model. b. Write the expressions for...
Assume there are no investment projects in the economy that yield an expected rate of return of 25 percent or more. But suppose there are $10 billion of investment projects yielding expected returns...
Should public employees of all types of jobs be allowed to strike?
Under the random utility interpretation, an individual with utility $U_{i j}=$ $u_{i}\left(V_{i j}+\epsilon_{i j} ight)$, where $j$ may be 1 or 2 , selects category corresponding to $j=1$...
Bayliner Company acquired a plant asset at the beginning of Year 1. The asset has an estimated service life of 5 years. An employee has prepared depreciation schedules for this asset using three...
1. For Firm G, compute cost of direct labor used. 2. For Firm G, compute cost of direct materials used. 3. For Firm G, compute cost of goods manufactured. 4. For Firm G, compute cost of goods sold....
A piece of string is connected between two adjacent houses to form a clothesline. The houses are separated by d = 22 m, and both ends of the string are the same height off the ground. A sweater is...
Consider the population regression of test scores against income and the square of income in Equation (8.1). a. Write the regression in Equation (8.1) in the matrix form of Equation (18.5). Define Y,...
Consider the problem of minimizing the sum of squared residuals subject to the constraint that Rb = r, where R is q (k + l) with rank q. Let be the value of b that solves the constrained...
Refer to the Farnsworth Company information in Problem 3-27. However, now assume that Tracy has used the method of least squares on the receiving data and found the following results:...
3. Duration Bank has the following assets and liabilities as of year-end. All assets and liabilities are currently priced at par and pay interest annually. Assets Amount ($ millions) Annual...
How does globalization intersect with environmental concerns, such as the depletion of natural resources, environmental degradation, and the exacerbation of climate change, and what are the...
discuss the challenges and opportunities of cultural preservation and revitalization in the face of globalization, urbanization, and cultural commodification, and how communities navigate the...
How does cultural hegemony shape power dynamics within societies, influencing dominant cultural norms, values, and representations, while also marginalizing and suppressing alternative cultural...
How do cultural anthropologists conceptualize and study culture, taking into account its dynamic and multi-dimensional nature, including its symbolic systems, social practices, and historical...
The type of jet engine used on most large commercial aircraft is called a turbofan jet engine because it has a large wheel at the front of the engine that propels air rearward. Most of this air...
In Exercises evaluate the limit, using LHpitals Rule if necessary. lim 07x cos x X
Analyze the following data by using a multiple regression computer software package to predict y using x1 and x2. Notice that x2 is a dummy variable. Discuss the output from the regression analysis;...
Given here are the data from a dependent variable and two independent variables. The second independent variable is an indicator variable with several categories. Hence, this variable is represented...
The Minitab output displayed here is the result of a multiple regression analysis with three independent variables. Variable x1 is a dummy variable. Discuss the computer output and the role x1 plays...
What is one specific security tactics to protect the network. Identify specific tools selections to accomplish compliance and audit requirement Describe how alerts would be collected and presented...
1. Solve each equation for x, where 0x & a) sin x-= 0 b) cosx-3 cosx+2=0
Explain Article III Standing, and explain how to achieve standing. b) Explain Negligence, and provide an example of a Negligence claim. c) What happened in the case of Genesco v. Visa? d) Explain the...

Suppose that C is an n n symmetric idempotent matrix with rank r and let a.

Question:

V~N(0 In)

Step by Step Answer:

a Using the hint C ...View the full answer

Introduction to Econometrics

Students also viewed these Statistics questions