1. For the simple prediction problem where Y has a strictly increasing, continuous CDF F(.) and μ = E(Y) exists and is finite and the decision space is D = R, determine the decision d that minimises the risk R(d) = E [L(d|Y)] for the asymmetric piecewise-linear loss function given by Sp(y-d) for d y and some 0 < p <1 (hint: we have already seen the case p = 0.5).
1. For the simple prediction problem where Y has a strictly increasing, continuous CDF F(.) and μ = E(Y) exists and is finite and the decision space is D = R, determine the decision d that minimises the risk R(d) = E [L(d|Y)] for the asymmetric piecewise-linear loss function given by Sp(y-d) for d y and some 0 < p <1 (hint: we have already seen the case p = 0.5).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![1. For the simple prediction problem where Y has a strictly increasing, continuous CDF F(.) and
μ = E(Y) exists and is finite and the decision space is D = R, determine the decision d that
minimises the risk
R(d) = E [L(d|Y)]
for the asymmetric piecewise-linear loss function given by
Sp(y - d)
(1 − p)(d — y)
and some 0 < p<1 (hint: we have already seen the case p = 0.5).
L(d\y)
=
for d<y,
for dy](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1652026a-6ba6-42d7-9e35-ad3e7516e1ec%2F1722066f-0b1d-4b75-ba9d-56010658688e%2Forxat2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. For the simple prediction problem where Y has a strictly increasing, continuous CDF F(.) and
μ = E(Y) exists and is finite and the decision space is D = R, determine the decision d that
minimises the risk
R(d) = E [L(d|Y)]
for the asymmetric piecewise-linear loss function given by
Sp(y - d)
(1 − p)(d — y)
and some 0 < p<1 (hint: we have already seen the case p = 0.5).
L(d\y)
=
for d<y,
for dy
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