## Riemannian integral approximations, Applied Statistics

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Investigate the use of fixed and percentile meshes when applying chi squared goodness-of- t hypothesis tests.

Apply the oversmoothing procedure to the LRL data. Compare the results of using the range and variance as measures of scale.

Find an oversmoothed rule based on the interquartile range as a measure of scale.

Use Taylor series and Riemannian integral approximations to verify

Carefully evaluate and verify the formulas in Equation. Hint : What are the UCV and BCV bin widths for the LRL and snowfall data?

The UCV rule seems to estimate something between ISE and MISE [the middle quantity, , being the focus]. Using the exact MISE formula with Normal and lognormal data, investigate the behavior of the terms in the UCV approximation.

Take a Normal sample of size 1,000. Apply increasing degrees of rounding to the data and compare the resulting UCV curves. At what point does the minimizer of UCV become h = 0?

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