[Solved] Stat435 Homework1-Kernel smoothing

Gain experience with Kernel smoothing

• Write a R function

ksmooth.train(x.train, y.train, kernel = c(box, normal), bandwidth = 0.5, CV = False)

The kernels should be scaled so that their quartiles (viewed as probability densities) are at 0.25 bandwidth.

The function should produce a list with components x.train and yhat.train.

If CV = True, training observation i should not be used in the calculation of yhat.train[i].

Do not assume that x.train is ordered. Try to be efficient!

• Write a R function predict(ksmooth.train.out, x.query)

The function should use linear interpolation inside the range ofx.train and constant extrapolation outside the range.

Note: Do not assume that x.query is ordered. Do not use the R function ksmooth.

I have randomly divided the Wage data from ISLR into a training set Wage.train of size 1000 and a test set of Wage.test of size 2000. The data are in the dump file home1-data.R that you can source.

• Produce a scatterplot of train vs age.train and add a kernel smooth for a normal kernel with bandwidth = 3. Print the residual sum of squares.
• Use the smooth computed above to predict test. Draw a scatterplot of wage.test vs age.test and add the smooth. Print the residual sum of squares.

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• Plot the resubstition estimate of the expected squared prediction error as a function of bandwidth for bandwidths = 1, 2,,10. Print the 10 values.
• Plot the LOOCV estimate of the expected squared prediction for the 10 bandwidths. and print the 10 values. What is the bandwidth you would choose?
• Plot the test set estimate of the expected suared prediction error for the 10 bandwidths and print the 10 values.
• Plot the 5-fold CV estimate of the expected squared prediction error for the 10 bandwidths and print the 10 values.

Use the assignment to training observations to folds defined by the variable fold in home1-data.R.