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Show that the ISB in a bin containing the origin of the double exponen-tial density, f(x) = exp(-|x|)/2, is O(h3); hence, the discontinuity in the derivative of f does not have any asymptotic e ect on consistency. Compare when 0 and h/2 are bin edges. Formally, if f is the ordinary negative exponential density, R(f') is in nite because of the jump at zero (integral of the square of the Dirac delta function at 0), but R(f') is well-de ned for the double exponential.
Consider the exact MISE of a histogram when f = U(0; 1).
(a) If the mesh tk = kh is chosen where h = 1/m, show that MISE(m, n) = (m - 1)/n.
(b) If tk = (k + 1/2 )h with h = 1/m, show that
(c) Conclude that
Verify the inequalities for the adaptive MISE.
Find the optimal adaptive meshes for a skewed Beta density using a numerical optimization program.
Random Sampling Method In this method the units are selected in such a way that every item in the whole universe has an equal chance of being included. In the words of croxton
The Maju Supermarket stocks Munchies Cereal. Demand for Munchies is 4,000 boxes per year and the super market is open throughout the year. Each box costs $4 and it costs the store
This probability rule determined by the research of the two mathematicians Bienayme' and Chebyshev, explains the variability of data about its mean when the distribution of the dat
For the data analysis project, you will address some questions that interest you with the statistical methodology we are learning in class. You choose the questions; you decide h
The interest rate on the three year loan is 0.087. Whereas the interest rate on the two year loan is 0.085 as given in A. Suppose that the liquidity premium at t=1 is 0.002 and tha
Cluster Analysis could be also represented more formally as optimization procedure, which tries to minimize the Residual Sum of Squares objective function: where μ(ωk) - is a centr
Explain any two applications of statistics
Choose any published database from the internet or Bethel library (such as those from the Census Bureau or any financial sites). You may opt to use one of the data files provided b
CALCULATE THE PERCENTAGE OF REFUNDS EXPECTED TO EXCEED $1000 UNDER THE CURRENT WITHHOLDING GUIDELINES
For many decades, there has been considerable attention paid to identifying various factors that help to reduce the number of fatalities on Australian roads. In 1964 Victoria and S
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