To describe a linear-time algorithm that solves the selection processes for an arbitrary order statistic.

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Chapter 9.3, Problem 5E

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To describe a linear-time algorithm that solves the selection processes for an arbitrary order statistic.

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Appendix A 10-Fold Cross Validation for Parameter Selection Cross Validation is the standard method for evaluation in empirical machine learning. It can also be used for parameter selection if we make sure to use the training set only. To select parameter A of algorithm A(X) over an enumerated range d E [A1,..., A] using dataset D, we do the following: 1. Split the data D into 10 disjoint folds. 2. For each value of A e (A1,..., Ar]: (a) For i = 1 to 10 Train A(A) on all folds but ith fold Test on ith fold and record the error on fold i (b) Compute the average performance of A on the 10 folds. 3. Pick the value of A with the best average performance Now, in the above, D only includes the training data and the parameter A is chosen without the knowledge of the test data. We then re-train on the entire train set D using the chosen A and evaluate the result on the test set.

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2. Use the rbinom() function to generate a random sample of size N = 50 from the bino- mial distribution Binomial(n, p), with n 6 and p = 0.3. Note that this distribution has mean u = np and standard deviation o = Vnp(1 – p). Record the obtained sample as a vector v. Repeat the tasks of Problem 1 for the sample v.