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日期:2019-03-27 10:18

Financial Econometrics: Assignment One

March 11, 2019

Due: 2018-10-11

1 KERNEL DENSITY ESTIMATOR

Step 1: Generate random numbers from standard Normal distribution with sample size T =1000.1 Let the generated sample be {x1,...,xT }.

Step 2: Let k(·) be the Epanechnikov kernel, i.e.,

For a fixed x0, the kernel density estimator is given b

where h is a bandwidth. In practice, kernel estimation is sensitive to the choice of h. In Step 2,

you are required to choose h based on the method called likelihood cross-validation, which

chooses h to maximize the log likelihood function given by

L =1Remember to set a seed before the random number generation.

1

is the leave-one-out kernel estimator of f (xt).

Step 3: Using the optimal bandwidth h obtained in Step 2, estimate the density function

evaluated at each sample point xt

, t = 1,...,T . Compare your result with standard normal

distribution.

2


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