516 polynomial approximation of inverse using

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Unformatted text preview: T x. The vector c ∈ Rn is the model parameter, which we want to choose. We will use a least-squares criterion, i.e., choose c to 48 minimize K J= k=1 y (k ) − c T x (k ) 2 . Here is the tricky part: some of the values of y (k) are censored; for these entries, we have only a (given) lower bound. We will re-order the data so that y (1) , . . . , y (M ) are given (i.e., uncensored), while y (M +1) , . . . , y (K ) are all censored, i.e., unknown, but larger than D, a given number. All the values of x(k) are known. (a) Explain how to find c (the model parameter) and y (M +1) , . . . , y (K ) (the censored data values) that minimize J . (b) Carry out the method of part (a) on the data values in cens_fit_data.m. Report c, the value ˆ of c found using this method. Also find cls , the least-squares estimate of c obtained by simply ignoring the censored data ˆ samples, i.e., the least-squares estimate based on the data (x(1) , y (1) ), . . . , (x(M ) , y (M ) ). The data file contains c...
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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.

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