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Unformatted text preview: n with rank n, with m ≥ n. We know y and A, but we don’t
know v ; our goal is to estimate x. We make only one assumption about the measurement error v :
v ∞ ≤ ǫ.
We will estimate x using a linear estimator x = By ; we must choose the estimation matrix B ∈
Rn×m . The estimation error is e = x − x. We will choose B to minimize the maximum possible
value of e ∞ , where the maximum is over all values of x and all values of v satisfying v ∞ ≤ ǫ.
(a) Show how to ﬁnd B via convex optimization.
(b) Numerical example. Solve the problem instance given in minimax_fit_data.m. Display the
x you obtain and report x − xtrue ∞ . Here xtrue is the value of x used to generate the
measurement y ; it is given in the data ﬁle.
6.12 Cox proportional hazards model. Let T be a continuous random variable taking on values in R+ .
We can think of T as modeling an event that takes place at some unknown future time, such as
the death of a living person or a machine failure.
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
- Fall '13
- The Aeneid