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# Parametric and Non-Parametric Methods Problem 1 You are given a dataset D = {0,1,1,1,2,2,2,2,3,4,4,4,5}. Using techniques from parametric and...

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Parametric and Non-Parametric Methods
Problem 1
You are given a dataset D = {0,1,1,1,2,2,2,2,3,4,4,4,5}. Using techniques from parametric
and non-parametric density estimation, answer the following questions:
1. Draw a histogram of D with a bin-width ofland bins centered at {0,1,2,3,4,5}.
2. Write the formula for the kernel density estimate given an arbitrary kernel K.
3. In terms of their respective algorithms and their asymptotic performance, compare
the Parzen window method and the k - NN method of non-parametric density
estimation.
4. Select a triangle kernel as your window function:
K(u) = (1-|up)6(|u| &lt; 1)
Where u is a function of the distance of sample x; to the value in question x divided
by the bandwidth: u = =1 Compute the kernel density estimates for the following
values of x = {0,1,2.3,4.5} bandwidths of 2.
5. Now, what if you make an assumption that, rather, the density is a parametric
density. it is a Gaussian Compute the maximum likelihood estimate of the
Gaussian's parameters.
Compare the
he histogram, the triangle-kernel density estimate, and the ma
likelihood estimated Gaussian. Which best captures the data? What does each miss?
Why would you choose one of another if you were forced to?

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