Lecture 2 Week 1 Kernel Density Estimator

Question 1

What are the main drawbacks of the histogram?

Answer 1

slide 4

Question 2

What is the kernel density estimator?
What is the idea of the kernel density?

Answer 2

slide 5

Question 3

How can the kernel density be rewritten?

Answer 3

slide 6

Question 4

What type of function is a kernel function?

Answer 4

slide 8

Question 5

What do the choice of the kernel and bandwidth to the kernel density estimate?

Answer 5

The kernel density estimate depends on the choice of the kernel
function

However, the bandwidth plays the major role in determining the
smoothness of the kernel density estimator

Question 6

What is the bias and the approximation of the bias and when does the bias go to 0?

Answer 6

slide 14

Question 7

What is the variance of the kernel density and the approximate expression for the variance?

Answer 7

slide 15

Question 8

What is the MSE and what is the interpretation of the MSE?

Answer 8

slide 16

Question 9

How is the trade-off between the bias and variance in selecting h given?

Answer 9

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Question 10

How to choose h?

Answer 10

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Question 11

What is the MISE and the approximate expression for MISE?

Answer 11

slide 20

Question 12

How is the optimal bandwidth given and the interpretation?

Answer 12

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Question 13

What is then the optimal bandwidth and what is a practical way to approximate the optimal h?

Answer 13

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Question 14

What is Silverman’s rule of thumb?

Answer 14

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Question 15

What is the rule of thumb bandwidth?

Answer 15

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Question 16

How to obtain the confidence intervals?

Answer 16

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Question 17

What is the asymptotic distribution?

Answer 17

slide 27

Question 18

What are then the confidence intervals?

Answer 18

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Question 19

What are the difference between confidence intervals and bands?

Answer 19

slide 29,30

Question 20

Kernel density in R

Answer 20

slide 33-37