Showing papers on "Expectation–maximization algorithm published in 1974"

A log gamma model and its maximum likelihood estimation

Abstract: SUMMARY A three parameter model is developed by reparameterizing and extending the distribution of the logarithm of a generalized gamma variate. The extreme value distributions for maxima and minima are included while the normal distribution is central. Asymptotic maximum likelihood theory is given and maximum likelihood distributions are studied, via simulation, in some special cases. A regression generalization is given.

Uniqueness of the maximum likelihood estimates of the parameters of an ARMA model

Abstract: Estimation of the parameters in a mixed autoregressive moving average process leads to a nonlinear optimization problem. The negative logarithm of the likelihood function, suitably normalized, converges to a deterministic function as the sample length increases. The local and global extrema of this function are investigated. Conditions for the existence of a unique global and local minimum are given.

Maximum Likelihood Estimation with the Weibull Model

Abstract: Some of the questions concerning the uniqueness of the maximum likelihood estimates for the parameters in the Weibull distribution are considered for both censored and noncensored samples. In some cases answers previously known are reviewed, while new results are presented for some other cases. In particular, it is shown that with the shape parameter known, the maximum likelihood estimates of the location and scale parameters exist and are unique. Also, the case in which all three parameters are unknown is examined in detail.

Log-Linear Models for Frequency Tables Derived by Indirect Observation: Maximum Likelihood Equations

Abstract: Frequency tables are examined in which some cells are not distinguishable. Log-linear models are proposed for these tables which lead to likelihood equations closely related to those associated with log-linear models for conventional frequency tables. Just as in conventional tables, the maximum likelihood equations are shown to be the same under Poisson or multinomial sampling. Applications are made to the problem of estimation of gene frequencies from observed phenotype frequencies.

Maximum likelihood estimates of the parameters of a mixture of two regression lines

Abstract: The method of maximum likelihood is used to estimate the parameters of a mixture of two regression lines, The results of a small simulation study show that when the sample size exceeds 250 and the regression lines are more than three standard deviations apart for at least one half of the data, the maximum likelihood estimates are reliable. When this is net the case their sampling variances are so large that the estimates may not be reliable.

A recursive (on-line) maximum likelihood identification method

Abstract: A recursive (on-line) identification algorithm is developed based upon the off-line maximum likelihood method by Astrom and Bohlin. The basic idea of the algorithm consists in two modifications to the classical method. First an approximate noisemodel is applied to eliminate auto-regressive filtering in the computation of the noise-derivatives. Second, some approximations are introduced to make the direct recursive version of the iteration equations really on-line. The combination of the two modifications yields a compact on-line algorithm.

Maximum likelihood estimation in the birth-and-death process

Abstract: : Maximum likelihood estimation of the parameters lambda and mu of a simple (linear) birth-and-death process observed continuously over a fixed time interval is studied. Asymptotic distributions for large initial populations and for large periods of observation are derived and some nonstandard results appear. The related problem of estimation from the discrete skeleton of the process is also discussed.

Statistical methods for absorbing Markov-chain models for learning: Estimation and identification

Abstract: General algorithms for computing the likelihood of any sequence generated by an absorbing Markov-chain are described These algorithms enable an investigator to compute maximum likelihood estimates of parameters using unconstrained optimization techniques The problem of parameter identifiability is reformulated into questions concerning the behavior of the likelihood function in the neighborhood of an extremum An alternative characterization of the concept of identifiability is proposed A procedure is developed for deciding whether or not this definition is satisfied

On the Maximum Likelihood Estimation of Stochastically Ordered Random Variates

Abstract: Brunk, Franck, Hanson and Hogg (1966) ("Maximum likelihood estimation of the distributions of two stochastically ordered random variables," J. Amer. Statist. Assoc. 61 1067-1080) found and studied maximum likelihood estimates of a pair of stochastically ordered distribution functions. In this paper we discuss a generalization of this problem in which we do not require the domain of these "distribution functions" to be the real line. We think of the order restriction we impose on these "distribution functions" as an analogue of stochastic ordering on the line. Maximum likelihood estimates are found and strong uniform consistency properties are discussed.

Moment-type estimation in the exponential family

Abstract: Some aspects of the Pearson-Fisher controversy concerning the method of moments and the method of maximum likelihood are reviewed. In the multiparameter exponential family, a modification of the method of moments which requires the estimators to be functions of the minimal sufficient statistic is discussed It is shown that these modified estimators are in fact the maximum likelihood estimators.Although the mathematics underlying the result is widely available in the literature, the authors have not seen it stated in the present context.

A note on the consistency of maximum likelihood estimators

Abstract: A sequence of maximum likelihood estimators based on a sequence of independent but not necessarily identically distributed random variables is shown to be consistent under certain assumptions. Some examples are given to show that these assumptions are easy to verify and not very restrictive.

Maximum Likelihood Estimation for the Multinomial Distribution Using Geometric Progamming

Abstract: The problem of obtaining maximum likelihood estimates for the multinomial distribution is considered. Maximum likelihood estimation is applied to the particular problem of estimating overlap sizes created by interlocking sampling frames. In this paper, geometric programming is discusseda as a method of solving the likelihood function and is applied to a practical example of estimating overlap sizes.

A General Algorithm for Simultaneous Estimation of Constant and Randomly-Varying Parameters in Lineal Relations

Abstract: A recursive algorithm for estimating linear models with both constant and time-varying parameters is derived by maximization of a likelihood function. Recursive formulas are also derived for derivatives of the likelihood function; the derivatives are needed for numerical evaluation of some parameters. Smoothing formulas are also derived. The estimation algorithm is compared with others for similar classes of models.

A Likelihood Analysis of Some Common Distributions

Abstract: Likelihood functions provide a convenient and useful means of summarizing the numerical information that the data has to offer about a parameter or a set of parameters. This paper introduces the concepts of likelihood and likelihood functions and uses t..

Maximum Likelihood Estimation in Quantal Response Experiments

Abstract: This paper is concerned with maximum likelihood estimates for the population parameters in experiments in which the responses are quantal and the distributions are assumed to be normal. A set of necessary and sufficient conditions is developed for the existence of a unique maximum of the likelihood function. A modified form of the Newton–Raphson procedure is described, for which global convergence can be proved for cases in which the given conditions are satisfied. These results extend the earlier developments of Golub and Grubbs.

Maximum Likelihood Methods

Abstract: In dealing with the problem of estimating the parameters of a structural system of equations, we had not, in previous chapters, explicitly stated the form of the density of the random terms appearing in the system. Indeed, the estimation aspects of classical least squares techniques and their generalization to systems of equations are distribution free, so that no explicit assumption need be made with respect to the distribution of the error terms. On the other hand, in considering various tests of significance on 2SLS or 3SLS estimated parameters of a structural system, we have occasionally found it convenient to assert (joint) normality of the structural error terms. Under this assumption, the derivation of the asymptotic distribution of such estimators is simplified considerably.