Question 4 Consider the simulated data set in the file Simdata1.mat. Compute the density estimates using the reference rule-of thumb in (1.9) on page 16 of the text book presuming an underlying normal distribution. 1. How many times larger than this would the bandwidth have to be to remove the bimodal feature present in the sample ? 2. Compute the density estimate using least-squares cross-validation. Presuming that these bandwidths represent the "optimal" bandwidths, how much larger would the bandwidth have to be to produce an apparently unimodal distribution ? 3. Compare your results least-squares cross-validated density estimates with a naive histogram. Do your estimates appear sensible i.e., do they reflect features you believe are in fact present in the data ? Question 4 Consider the simulated data set in the file Simdata1.mat. Compute the density estimates using the reference rule-of thumb in (1.9) on page 16 of the text book presuming an underlying normal distribution. 1. How many times larger than this would the bandwidth have to be to remove the bimodal feature present in the sample ? 2. Compute the density estimate using least-squares cross-validation. Presuming that these bandwidths represent the "optimal" bandwidths, how much larger would the bandwidth have to be to produce an apparently unimodal distribution ? 3. Compare your results least-squares cross-validated density estimates with a naive histogram. Do your estimates appear sensible i.e., do they reflect features you believe are in fact present in the data