Question: For an arbitrary random variable Y and a ?-algebra F A, generated by observing some event A, the variance decomposition holds. Show that the unconditional

For an arbitrary random variable Y and a ?-algebra FA, generated by observing some event A, the variance decomposition

Var[ Y] = Var[E[ YF4]] + E[Var[ Y[FA] %3D Var[l}] =oE[(X X)-"),

holds. Show that the unconditional variance of the least-squares estimator|??? is

image

where X is the usual data matrix, containing a column of ones and the regressors Xt, for t = 1, . . . , T.

Var[ Y] = Var[E[ YF4]] + E[Var[ Y[FA] %3D Var[l}] =oE[(X X)-"),

Step by Step Solution

★★★★★

3.41 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Starting from the equation EXX1 XY where is the OLS estimator we can calculate the unconditional ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Marketing Strategy Planning Questions!

Q:

Random variable Y = X - Z is a noisy observation of the continuous random variable X. The noise Z has zero expected value and unit variance and is independent of X. Find the conditional expectation...

Q:

For a Student t random variable Y with n degrees of freedom and any positive integer k, show that E(Y 2k ) exists if 2k 0, > 0, and > 1.) 00 1 dy (1+y")

Q:

Let X be a Gaussian random variable with zero mean and arbitrary variance, 2. Given the transformation Y= X3, find fY (y).

Q:

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Q:

,.kindly solve please 1. Consider the simple regression model: V/i = Po+ Piri +ui, for i = 1, ..., n, with E(ur,) 7 0 and let z be a dummy instrumental variable for a, such that we can write: with...

Q:

1 2.3 Definition of a Discrete Probability Function Definition: Let S be a discrete sample space from some experiment. A function P, defined on all events in S, is said to be a probability function...

Q:

(a) In SystemVerilog, what is the difference between: (i) The ternary operator ? and if...then...else statements? [2 marks] (ii) always_ff and always_comb? [2 marks] (iii) Blocking, non-blocking and...

Q:

Submitted to Management Science manuscript MS-0001-1922.65 Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title....

Q:

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

Q:

When you identified income statement fluctuations in steps (e) and (f) of this assignment, which information did you find most helpfulcomparisons of the current year's and prior year's balances, or...

Q:

Best Motors has hired Robert Trent as its new president. Terms included the companys agreeing to pay retirement benefits of $17,900 at the end of each semiannual period for 12 years. This will begin...

Q:

Changes in stock prices: A) do not affect people"s wealth and their willingness to spend. B) affect firms' decisions to sell stock to finance investment spending. C) occur in regular patterns. D) are...

Q:

spreadsheet above. Selected assumptions are given for preparing pro forma financial statements for 2022. Assume that no new equity will be issued and that no equity will be repurchased in 2022. When...

Q:

5. In his current job, Smith can work as many hours per day as he chooses, and he will be paid $1/hr for the first 8 hours he works, $2.50/hr for each hour over 8. Faced with this payment schedule,...

Q:

For the first five months of its existence (August through December 2018), the Estate of Amy Ennis had gross income (net of expenses) of $7,000 per month. For January through July 2019, the executor...

Q:

A complex trust has taxable income of $29,900 in 2018. The $29,900 includes $5,000 of rental income and $25,000 of taxable interest income, reduced by the $100 personal exemption. The trust makes no...

Q:

Suellen Symmes died on January 15, 2018. Her estate elected a November 30 year end. The executor projects that the estate will receive interest income of $50,000 by November 30, 2018, and will have...

Q:

Firm P/B Forecasted ROE A 10% B 2 12% C 1 9% Based on the information above, which of the following statements is most likely to be correct? Select one: O a. Company B is overvalued relative to...

Q:

6. Write the MIPS assembly code that corresponds to the pseudo code below. Assume that the address for integer i is baseaddress +4 and the address for a[0] is baseaddress +8. Assume that the...

Q:

Consider the following two mutually exclusive projects: Year o 1 2 3 Cash Flow (X) -$23,900 13,100 9,480 7,890 Cash Flow (Y) -$23,900 9,300 10,620 11,180 a. What is the IRR of Project X? (Do not...