Kindly I need some help

2. Use R to conduct a Monte Carlo experiment comparing both correct and incor- rect parametric estimation of a probability density function against that for a kernel density estimator. (a) Specifically, let X ~ x? where v = 100 and generate samples of n =25, 50, 100, 200, 400, 800, 1,600, 3,200, 6,400, and 12,800 for M = 1, 000 Monte Carlo replications. Use a Gaussian kernel with Silverman rule-of-thumb November 2, 2020 2 bandwidth for your nonparametric density estimator. For each sample size, calculate over a fine grid, the median root mean squared error of your correctly specified parametric density estimator (v can be calculated via the sample mean) and the nonparametric density estimator. Then run a regression of the logarithm of median RMSE against logarithm of n. The coefficient estimate from this regression is the approximate rate of convergence. If you have done things correctly the correctly specified parametric model should have a slope coefficient of approximately -0.5 while for the nonparametric estimator the slope coefficient should be ap- proximately -0.4. You can use a method of moments estimator for the degrees of freedom for the x? distribution. (b) Now estimate a Gaussian model, estimating the mean and variance, from the previous setup. What is the slope coefficient from the regression of logarithm of median RMSE against logarithm n in this case? (c) What is the order of magnitude of the parametric Gaussian model com- pared to the nonparametric estimator? Does your Gaussian estimator appear to be statistically consistent based on your simulations? Why is this? (d) Can the Gaussian estimator be consistent in the statistical sense