This topic contains a solution. Click here to go to the answer

Author Question: Unbiasedness and small variance are desirable properties of estimators. However, you can imagine ... (Read 190 times)

skymedlock

  • Hero Member
  • *****
  • Posts: 561
Unbiasedness and small variance are desirable properties of estimators.
 
  However, you can imagine situations where a trade-off exists between the two: one estimator may be have a small bias but a much smaller variance than another, unbiased estimator. The concept of mean square error estimator combines the two concepts. Let be an estimator of . Then the mean square error (MSE) is defined as follows: MSE( ) = E(  )2. Prove that MSE( ) = bias2 + var( ). (Hint: subtract and add in E( ) in E(  )2.)
  What will be an ideal response?

Question 2

In a multiple regression framework, the slope coefficient on the regressor X2i
 
  A) takes into account the scale of the error term.
  B) is measured in the units of Yi divided by units of X2i.
  C) is usually positive.
  D) is larger than the coefficient on X1i.



Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question
Marked as best answer by a Subject Expert

jonathanballen97

  • Sr. Member
  • ****
  • Posts: 347
Answer to Question 1

Answer:
MSE ( ) = E( - E( ) + E( ) - )2 = E( - E( )) + (E( ) - )2
= E( - E( ))2 + (E( ) - )2 + 2( - E( ))(E( ) - )
Next, moving through the expectation operator results in
E - E( )2 + EE( ) - )2 + 2E( ) - E( ))( E( ) - ).
The first term is the variance, and the second term is the squared bias, since
EE( ) - )2 = E( ) - )2. This proves MSE ( ) = bias2 + var( ) if the last term equals zero. But
E( - E( ))(E( ) - ) = EE( ) -  - (E( ))2 + E( )
= E( ) E( ) - E( ) - (E( ))2 + E( ) = 0.

Answer to Question 2

Answer: B




skymedlock

  • Member
  • Posts: 561
Reply 2 on: Jun 29, 2018
Great answer, keep it coming :)


mjenn52

  • Member
  • Posts: 351
Reply 3 on: Yesterday
YES! Correct, THANKS for helping me on my review

 

Did you know?

As many as 28% of hospitalized patients requiring mechanical ventilators to help them breathe (for more than 48 hours) will develop ventilator-associated pneumonia. Current therapy involves intravenous antibiotics, but new antibiotics that can be inhaled (and more directly treat the infection) are being developed.

Did you know?

The term pharmacology is derived from the Greek words pharmakon("claim, medicine, poison, or remedy") and logos ("study").

Did you know?

According to the FDA, adverse drug events harmed or killed approximately 1,200,000 people in the United States in the year 2015.

Did you know?

Eating carrots will improve your eyesight. Carrots are high in vitamin A (retinol), which is essential for good vision. It can also be found in milk, cheese, egg yolks, and liver.

Did you know?

Your chance of developing a kidney stone is 1 in 10. In recent years, approximately 3.7 million people in the United States were diagnosed with a kidney disease.

For a complete list of videos, visit our video library