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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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Large Sample Test for Mean A random sample of size n (n > 30) has a sample mean . To test the hypothesis that the population mean μ has a specified value μ 0 let us formu
The mean tax-return preparation fee H&R Block charged retail customers in 2012 was $183 (The Wall Street Journal, March 7, 2012). Use this price as the population mean and assume t
Accelerated Failure Time Model A basic model for the data comprising of survival times, in which the explanatory variables measured on an individual are supposed to act multipli
Application of the chi Square Test
discuss the mathematical test of adequacy of index number of formulae. prove algebraically that the laspeyre, paasche and fisher price index formulae satisfies this test. What is
Mean Absolute Deviation To avoid the problem of positive and negative deviations canceling out each other, we can use the Mean Absolute Deviation which is given by
Test for Equality of Proportions For example, we may want to test whether the percentage of smokers (p 1 ) among the males equals the percentage of female smokers (p 2 ). W
Simple Linear Regression One calculate of the risk or volatility of an individual stock is the standard deviation of the total return (capital appreciation plus dividends) over
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