Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

Name: Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems
Brand: Biblioscholar
SKU: 9781288915491
Price: 16.99 EUR
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Autor: Patrick Charles Murphy

Jazyk:

Väzba: Brožovaná

Vydavateľ: Biblioscholar

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An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approx...

Informácie o knihe

Autor

Patrick Charles Murphy

Jazyk

Angličtina

Väzba

Kniha - Brožovaná

Vydalo

2013

Stránok

116

EAN

9781288915491

ISBN

9781288915491

Enbook ID

08287342

Vydavateľ

Biblioscholar

Hmotnosť

222

Rozmery

189 x 246 x 6

Kompletný popis

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

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Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

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