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Fisher Information Matrix (fisher + information_matrix)

Distribution by Scientific Domains

Mathematics and Statistics	80%

Selected Abstracts

Fisher Information Matrix of the Dirichlet-multinomial Distribution

BIOMETRICAL JOURNAL, Issue 2 2005
Sudhir R. Paul
Abstract In this paper we derive explicit expressions for the elements of the exact Fisher information matrix of the Dirichlet-multinomial distribution. We show that exact calculation is based on the beta-binomial probability function rather than that of the Dirichlet-multinomial and this makes the exact calculation quite easy. The exact results are expected to be useful for the calculation of standard errors of the maximum likelihood estimates of the beta-binomial parameters and those of the Dirichlet-multinomial parameters for data that arise in practice in toxicology and other similar fields. Standard errors of the maximum likelihood estimates of the beta-binomial parameters and those of the Dirichlet-multinomial parameters, based on the exact and the asymptotic Fisher information matrix based on the Dirichlet distribution, are obtained for a set of data from Haseman and Soares (1976), a dataset from Mosimann (1962) and a more recent dataset from Chen, Kodell, Howe and Gaylor (1991). There is substantial difference between the standard errors of the estimates based on the exact Fisher information matrix and those based on the asymptotic Fisher information matrix. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Skew-symmetric distributions generated by the distribution function of the normal distribution

ENVIRONMETRICS, Issue 4 2007
Héctor W. Gómez
Abstract In this paper we study a general family of skew-symmetric distributions which are generated by the cumulative distribution of the normal distribution. For some distributions, moments are computed which allows computing asymmetry and kurtosis coefficients. It is shown that the range for asymmetry and kurtosis parameters is wider than for the family of models introduced by Nadarajah and Kotz (2003). For the skew- t -normal model, we discuss approaches for obtaining maximum likelihood estimators and derive the Fisher information matrix, discussing some of its properties and special cases. We report results of an application to a real data set related to nickel concentration in soil samples. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Quantum measurement and information

FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 2-3 2003
Z. Hradil
The operationally defined invariant information introduced by Brukner and Zeilinger is related to the problem of estimation of quantum states. It quantifies how the estimated states differ in average from the true states in the sense of Hilbert-Schmidt norm. This information evaluates the quality of the measurement and data treatment adopted. Its ultimate limitation is given by the trace of inverse of Fisher information matrix. [source]

Maximum likelihood estimation of higher-order integer-valued autoregressive processes

JOURNAL OF TIME SERIES ANALYSIS, Issue 6 2008
Ruijun Bu
Abstract., In this article, we extend the earlier work of Freeland and McCabe [Journal of time Series Analysis (2004) Vol. 25, pp. 701,722] and develop a general framework for maximum likelihood (ML) analysis of higher-order integer-valued autoregressive processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is binomial. A recursive representation of the transition probability of the model is proposed. Based on this transition probability, we derive expressions for the score function and the Fisher information matrix, which form the basis for ML estimation and inference. Similar to the results in Freeland and McCabe (2004), we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. Using the INAR(2) specification with binomial thinning and Poisson innovations, we examine both the asymptotic efficiency and finite sample properties of the ML estimator in relation to the widely used conditional least squares (CLS) and Yule,Walker (YW) estimators. We conclude that, if the Poisson assumption can be justified, there are substantial gains to be had from using ML especially when the thinning parameters are large. [source]

On the Evaluation of the Information Matrix for Multiplicative Seasonal Time-Series Models

JOURNAL OF TIME SERIES ANALYSIS, Issue 2 2006
E. J. Godolphin
Abstract., This paper gives a procedure for evaluating the Fisher information matrix for a general multiplicative seasonal autoregressive moving average time-series model. The method is based on the well-known integral specification of Whittle [Ark. Mat. Fys. Astr. (1953) vol. 2. pp. 423,434] and leads to a system of linear equations, which is independent of the seasonal period and has a closed solution. It is shown to be much simpler, in general, than the method of Klein and Mélard [Journal of Time Series Analysis (1990) vol. 11, pp. 231,237], which depends on the seasonal period. It is also shown that the nonseasonal method of McLeod [Biometrika (1984) vol. 71, pp. 207,211] has the same basic features as that of Klein and Mélard. Explicit solutions are obtained for the simpler nonseasonal and seasonal models in common use, a feature which has not been attempted with the Klein,Mélard or the McLeod approaches. Several illustrations of these results are discussed in detail. [source]

Real-time adaptive sequential design for optimal acquisition of arterial spin labeling MRI data

MAGNETIC RESONANCE IN MEDICINE, Issue 1 2010
Jingyi Xie
Abstract An optimal sampling schedule strategy based on the Fisher information matrix and the D-optimality criterion has previously been proposed as a formal framework for optimizing inversion time scheduling for multi-inversion-time arterial spin labeling experiments. Optimal sampling schedule possesses the primary advantage of improving parameter estimation precision but requires a priori estimation of plausible parameter distributions that may not be available in all situations. An adaptive sequential design approach addresses this issue by incorporating the optimal sampling schedule strategy into an adaptive process that iteratively updates the parameter estimates and adjusts the optimal sampling schedule accordingly as data are acquired. In this study, the adaptive sequential design method was experimentally implemented with a real-time feedback scheme on a clinical MRI scanner and was tested in six normal volunteers. Adapted schedules were found to accommodate the intrinsically prolonged arterial transit times in the occipital lobe of the brain. Simulation of applying the adaptive sequential design approach on subjects with pathologically reduced perfusion was also implemented. Simulation results show that the adaptive sequential design approach is capable of incorporating pathologic parameter information into an optimal arterial spin labeling scheduling design within a clinically useful experimental time. Magn Reson Med, 2010. © 2010 Wiley-Liss, Inc. [source]

A Pareto model for classical systems

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2008
Saralees Nadarajah
Abstract A new Pareto distribution is introduced for pooling knowledge about classical systems. It takes the form of the product of two Pareto probability density functions (pdfs). Various structural properties of this distribution are derived, including its cumulative distribution function (cdf), moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, maximum likelihood estimates and the Fisher information matrix. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Optimal designs for parameter estimation of the Ornstein,Uhlenbeck process

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 5 2009
Maroussa Zagoraiou
Abstract This paper deals with optimal designs for Gaussian random fields with constant trend and exponential correlation structure, widely known as the Ornstein,Uhlenbeck process. Assuming the maximum likelihood approach, we study the optimal design problem for the estimation of the trend µ and the correlation parameter , using a criterion based on the Fisher information matrix. For the problem of trend estimation, we give a new proof of the optimality of the equispaced design for any sample size (see Statist. Probab. Lett. 2008; 78:1388,1396). We also show that for the estimation of the correlation parameter, an optimal design does not exist. Furthermore, we show that the optimal strategy for µ conflicts with the one for ,, since the equispaced design is the worst solution for estimating the correlation. Hence, when the inferential purpose concerns both the unknown parameters we propose the geometric progression design, namely a flexible class of procedures that allow the experimenter to choose a suitable compromise regarding the estimation's precision of the two unknown parameters guaranteeing, at the same time, high efficiency for both. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Fisher Information Matrix of the Dirichlet-multinomial Distribution

Standard Errors for EM Estimates in Generalized Linear Models with Random Effects

BIOMETRICS, Issue 3 2000
Herwig Friedl
Summary. A procedure is derived for computing standard errors of EM estimates in generalized linear models with random effects. Quadrature formulas are used to approximate the integrals in the EM algorithm, where two different approaches are pursued, i.e., Gauss-Hermite quadrature in the case of Gaussian random effects and nonparametric maximum likelihood estimation for an unspecified random effect distribution. An approximation of the expected Fisher information matrix is derived from an expansion of the EM estimating equations. This allows for inferential arguments based on EM estimates, as demonstrated by an example and simulations. [source]