Showing papers on "Expectation–maximization algorithm published in 1972"
TL;DR: In this article, it was shown that there exists a simple, exact relationship between maximum entropy spectra and maximum likelihood spectra when the correlation function is known at uniform intervals of lag.
Abstract: In a long needed paper, R. T. Lacoss (1971) has presented many examples of spectra obtained by the maximum likelihood method and by the maximum entropy method and has shown that these newer techniques are in general superior to the more conventional spectral analysis methods. This short note shows that there exists a simple, exact relationship between maximum entropy spectra and maximum likelihood spectra when the correlation function is known at uniform intervals of lag. The data are of this form in almost all practical cases of time series analysis as well as in the special case of wavenumber spectral analysis of wave propagation as seen by a linear array of equally spaced sensors. The wavenumber case will be explicitly considered in this note since it requires the complex variable form of the theory.
382 citations
TL;DR: In this article, the exact finite-sample distribution of the limited-information maximum likelihood estimator when the structural equation being estimated contains two endogenous variables and is identifiable in a complete system of linear stochastic equations is derived.
Abstract: This article is concerned with the exact finite-sample distribution of the limited-information maximum likelihood estimator when the structural equation being estimated contains two endogenous variables and is identifiable in a complete system of linear stochastic equations. The density function derived, which is represented as a doubly infinite series of a complicated form, reveals the important fact that for arbitrary values of the parameters in the model, the LIML estimator does not possess moments of order greater than or equal to one
91 citations
TL;DR: In this paper, the authors investigated statistical properties of the bivariate exponential distribution and compared them with the estimates given by Arnold, showing that the method of moments type estimates are easy to compute and highly efficient, whereas the maximum likelihood estimates are computationally inconvenient.
Abstract: Statistical properties of the bivariate exponential distribution are investigated. Maximum likelihood and method of moments type estimates are obtained and compared with the estimates given by Arnold. The method of moments type estimates are easy to compute and highly efficient, whereas the maximum likelihood estimates are computationally inconvenient. The problem of testing for correlation in the bivariate exponential distribution is also investigated.
86 citations
TL;DR: In this article, it is shown that the maximum likelihood estimator of the reliability is very nearly unbiased and its variance is near the Cramer-Rao lower bound for the shape parameter.
Abstract: In life testing experiments it is a fairly common practice to terminate the experiment before all items have failed. The Weibull distribution is often used as a model for the observations and when a computer is available maximum likelihood estimation of the parameters is to be recommended. The tables presented in this paper enable one to set confidence limits on the parameters and the reliability based on the maximum likelihood estimates for selected censoring and sample sizes. It is also observed that, as in the case with no censoring, the maximum likelihood estimator of the reliability is very nearly unbiased and its variance is near the Cramer-Rao lower bound, Unbiasing factors for the maximum likelihood estimator of the shape parameter are given.
63 citations
59 citations
TL;DR: In this article, an iterative procedure is given for joint maximum likelihood estimation of the three parameters of the Weibull population, where the likelihood function is forned and the maximum likelihood equations are obtained.
Abstract: An iterative procedure is given for joint maximum likelihood estimation of the three parameters of the Weibull population. For this population, the likelihood function is forned and the maximum likelihood equations are obtained. Simultaneous solution of these equations yields joint maximum likelihood estimators for the three parameters. The proposed iterative procedure is a modified quasilinearization algorithm for solving nonlinear equations with bounded variables. Numerical results are given in which the parameters are estimated from real and from simulated life test data drawn from the Weibull population.
35 citations
TL;DR: In this article, an iterative method for obtaining maximum likelihood estimates of the structural and incidental parameters is proposed, and closed form expressions in terms of the ξ are obtained for the asymptotic covariance matrix of estimates of α and the scale incidental parameters σ, p and τ.
Abstract: SUMMARY: The problem considered is that of estimating a p-parameter functional relationship η = η(ξ;α, ..., α given replicated observations at each of n unknown values of the independent variable ξ. The errors of observation at (ξ, η) are assumed to have a bivariate normal distribution involving parameters σ, p and r and to be independent of those at any other true point. An iterative method for obtaining maximum likelihood estimates of the structural and incidental parameters is proposed. Closed form expressions in terms of the ξ are obtained for the asymptotic covariance matrix of estimates of the structural parameters α and the scale incidental parameters σ, p and τ. An illustrative application to simulated data and a discussion of convergence are included.
31 citations
Book•
01 Jan 1972
TL;DR: In this paper, maximum likelihood theory and applications for distributions generated when observing a function of an exponential family variable are discussed. But the authors focus on the distribution generated by observing the family variable.
Abstract: Maximum likelihood theory and applications for distributions generated when observing a function of an exponential family variable
22 citations
18 citations
TL;DR: In this article, it is shown that this likelihood is a poorly chosen approximation, in that an alternative form is exact for linear functions, and that an iterative procedure for maximizing the likelihood is unsatisfactory in comparison with more conventional methods.
Abstract: An approximate likelihood function has been suggested by Clutton-Brock for fitting a curve to data in the case where both the independent and dependent variables are subject to error. His iterative procedure for maximizing the likelihood is shown to be unsatisfactory in comparison with more conventional methods. It is also shown that this likelihood is a poorly chosen approximation, in that an alternative form is exact for linear functions.
TL;DR: In this paper, the authors studied the asymptotic behavior of the joint distribution and moments of generalized Bayesian estimates, maximum likelihood estimates and maximum probability estimates with respect to intervals constructed from independent observations with a density having a discontinuity of the first kind.
Abstract: In this paper the authors study the asymptotic behavior of the joint distribution and moments of generalized Bayesian estimates, maximum likelihood estimates and maximum probability estimates with respect to intervals constructed from independent observations with a density having a discontinuity of the first kind. Bibliography: 9 entries.
TL;DR: In this article, the aeromagnetic field is assumed to be a Gaussian random function and the probability density function of the log-radial spectrum is shown to be an asymmetric non-Gaussian function.
Abstract: Starting from the assumption that the aeromagnetic field is a Gaussian random function the probability density function of log-radial spectrum is shown to be a slightly asymmetric non-Gaussian function, [2q/2 Γ(q/2)]−1q(q/2)−1 exp(q/2(r-exp(r))). The depth to magnetic layer is determined by maximum likelihood (ML) technique and is compared with the least square (LS) estimate. The difference between the two is only marginal, about 15%. The least square estimate is lower than the maximum likelihood estimate.
TL;DR: A computer program is described which uses the maximum likelihood method to fit data which obey Poisson fluctuation with the following function N = ∑ ν A ν exp> (−α ν t) .