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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 eect 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.
Measurement of trend , least square method
What would be the cutoff score to indicate a score that is in the top 15% of the scores on a test with a mean of 100 and a standard deviation of 15? This question has multiple p
The range of actuator design parameters have been provisionally assessed and are presented in Table (3). You are required to determine the following parameters: The circumfer
(1) What values can the response variable Y take in logistic regression, and hence what statistical distribution does Y follow? The response variable can take the value of either
How do you change the base of the index
To compare three brands of computer keyboards, four data entry specialists were randomly selected. Each specialist used all three keyboards to enter the same kind of text material
Differentiate between data and database
Coefficient of Determination The coefficient of determination is given by r 2 i.e., the square of the correlation coefficient. It explains to what extent the variation
For calculating the mode of the grouped data graphically, the following procedure is adopted. Draw a histogram of the data; the modal class is the tallest rectangle.
construction of control chart,n chart
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