bv_cvxbook_extra_exercises

Assuming log p is dierentiable in show that 1k 1k x1

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Unformatted text preview: rse) are given in the cell array f. Hints. • You can represent each regressor function fj as a linear combination of the basis functions b0 (u) = u and bi (u) = (u − pk )+ − (−pk )+ for k = 1, 2, . . . , K , where (a)+ = max{a, 0}. • You might find the matrix XX = [b0 (X) b1 (X) · · · bK (X)] useful. 51 6 Statistical estimation 6.1 Maximum likelihood estimation of x and noise mean and covariance. Consider the maximum likelihood estimation problem with the linear measurement model yi = a T x + v i , i i = 1, . . . , m. The vector x ∈ Rn is a vector of unknown parameters, yi are the measurement values, and vi are independent and identically distributed measurement errors. In this problem we make the assumption that the normalized probability density function of the errors is given (normalized to have zero mean and unit variance), but not their mean and variance. In other words, the density of the measurement errors vi is p( z ) = 1 z−µ f( ), σ σ where f is a given, normalize...
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