Abstract
By Theorem 3.16, our task is to minimize the (real analytic, transcendentally nonlinear) strictly convex functional \({\rm h_n}(\vec{\theta})\) on the open convex set Θn. For numerical work, we must employ the functional \({\rm h_n}(\theta):=\log [\hat{\rm Z}_{\rm n}(\vec{\theta})] - \rm \sum\limits_{k = 1}^n {\theta _k r_k}\) and {ck, 0 ≤ k ≤ Nt} is determined by recursive relation (3.16.3)-(3.16.4) for some judicious truncation point Nt ≤ ∞. Recall that {rk,1 ≤ k ≤ n} is given for n ≤ N.
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© 1983 Springer-Verlag New York Inc.
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Britton, W. (1983). Solving for \({\vec \theta ^{(n)}}:n > 1\). In: Conjugate Duality and the Exponential Fourier Spectrum. Lecture Notes in Statistics, vol 18. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5528-4_6
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DOI: https://doi.org/10.1007/978-1-4612-5528-4_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90826-7
Online ISBN: 978-1-4612-5528-4
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