Let y represent an n x 1 observable random vector that follows the general mixed linear model y-XB+Z1s1 +Zcsc + e, where B is a p x 1 vector of unknown parameters, s, is a q1 x 1 unobservable random vector whose distr...
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We discuss a regression model in which the regressors are dummy variables. The basic idea is that the observation units can be assigned to some well‐defined combination of treatments, corresponding to the dummy varia...
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Two algorithms are compared for maximizing the likelihood function associated with parameter estimation in partially observed diffusion processes: • • the em algorithm, investigated by Dembo and Zeitouni (...
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Two algorithms are compared for maximizing the likelihood function associated with parameter estimation in partially observed diffusion processes: • • the em algorithm, investigated by Dembo and Zeitouni (1986), an iterative algorithm where, at each iteration, an auxiliary function is computed and maximized; • • the direct approach where the likelihood function itself is computed and maximized. This yields to a comparison of nonlinear smoothing and nonlinear filtering for computing a class of conditional expectations related to the problem of estimation. In particular, it is shown that smoothing is indeed necessary for the em algorithm approach to be efficient. Time discretization schemes for the stochastic PDE's involved in the algorithms are given, and the link with the discrete time case (hidden Markov model) is explored. Numerical results are presented with the conclusion that direct maximization should be preferred whenever some noise covariances associated with the parameters to be estimated are small.
The em algorithm is a numerical technique for the evaluation of maximum likelihood estimates for parameters describing incomplete data models. It is easy to apply in many problems and is stable but slow. The algorithm...
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The em algorithm is a numerical technique for the evaluation of maximum likelihood estimates for parameters describing incomplete data models. It is easy to apply in many problems and is stable but slow. The algorithm fails to provide a consistent estimator of the standard errors of the maximum likelihood estimates unless the additional analysis required by the Louis method is performed. Newton-type or other gradient methods are faster and provide error estimates but tend to be unstable and require the analytical evaluation of likelihoods to derive expressions for the score function and (at least) approximations to the Fisher information matrix. The purpose of this paper is to expand on a result by Fisher that permits a unification of em methodology and Newton methods. The evaluation of the individual observation-by-observation score functions of the incomplete data is a by-product of the application of the E step of the em algorithm. Once these become available, the Fisher information matrix may be consistently estimated, and the M step may be replaced by a fast Newton-type step.
In this paper a new method called the emS algorithm is used to solve Wicksell's corpuscle problem, that is the determination of the distribution of the sphere radii in a medium given the radii of their profiles in...
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From a cancer registry in the San Francisco Bay area we obtained survival data for 2,495 women diagnosed with breast cancer at ages 55-64. We relate mortality among these women to the time since diagnosis and to the s...
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From a cancer registry in the San Francisco Bay area we obtained survival data for 2,495 women diagnosed with breast cancer at ages 55-64. We relate mortality among these women to the time since diagnosis and to the stage of the disease at diagnosis. We divide the study period, extending through 10 years, into five two-year periods, and for each stage we assume a constant hazard rate during each of these periods. Let λ = (λjk) be the J × K matrix of hazard rates for the J = 5 periods and K = 5 stages. The most general model allows λjk to vary freely. A plot of maximum likelihood estimates of the hazard rates shows some tendency for increase with stage, but no simple patterns or parallelism across stage. We seek more restrictive models, to get simpler interpretations. The exponential model assumes that although λjk may vary with stage, it is constant over the five periods for each stage. This model, which assumes no dependence of hazard rate on time since diagnosis, is quite restrictive and indeed the likelihood ratio test of the exponential versus the general model rejects it strongly. Not quite as restrictive as the exponential model is a proportional-hazards model, which assumes that the log-hazard rates for the first four stages are parallel. Nevertheless, the likelihood ratio test of this model versus the general model rejects it as well. We explore the possibility that one of the more restrictive models is appropriate but that the bad fit is due to errors in staging. To do so, we replace the aforementioned models with ones that accommodate stage misclassification. Using the em algorithm to compute maximum likelihood estimates and likelihood ratio statistics, we find that the exponential model is again rejected, but that the proportional-hazards model fits the data. This example shows that simple models with straightforward interpretations might be discarded needlessly if covariate misclassifications are ignored. Simulations support this possibility. When data a
A robust procedure for estimating the five parameters of a mixture of two normals is proposed. The procedure is based on a robustification of the steps of the em algorithm. This results in the use of an iteratively re...
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A robust procedure for estimating the five parameters of a mixture of two normals is proposed. The procedure is based on a robustification of the steps of the em algorithm. This results in the use of an iteratively reweighted median and MAD. Simulation results are presented that show the superiority of the robustified em when compared to the usual em algorithm estimates.
The paper investigates parameter estimation for the Gibbs chain and for the partially observed Gibbs chain. A recursion technique is used for maximizing the likelihood function and for carrying out the em algorithm wh...
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The paper investigates parameter estimation for the Gibbs chain and for the partially observed Gibbs chain. A recursion technique is used for maximizing the likelihood function and for carrying out the em algorithm when only noisy data are available. Asymptotic properties are discussed and simulation results are presented.
作者：
HELLER, GSIMONOFF, JSNYU
LEONARD N STERN SCH BUSINESS DEPT STAT & OPERAT RES NEW YORK NY 10006 USA
Several methods of estimating parameters in a linear regression when the response variable is censored are compared. The estimator of Buckley and James (1979) is preferred. Further, it is shown that the strength of th...
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Several methods of estimating parameters in a linear regression when the response variable is censored are compared. The estimator of Buckley and James (1979) is preferred. Further, it is shown that the strength of the regression, the support and distribution of the censoring variable, and the magnitude of the slope all have an effect on the relative performance of the estimators.
作者：
GROSS, ALCUNY
GRAD CTRDEPT EDUC PSYCHOL33 W 42 STNEW YORKNY 10036 USA
A maximum likelihood approach is described for estimating the validity of a test (x) as a predictor of a criterion variable (y) when there are both missing and censoredy scores present in the data set. The missing dat...
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A maximum likelihood approach is described for estimating the validity of a test (x) as a predictor of a criterion variable (y) when there are both missing and censoredy scores present in the data set. The missing data are due to selection on a latent variable (y s ) which may be conditionally related toy givenx. Thus, the missing data may not be missing random. The censoring process in due to the presence of a floor or ceiling effect. The maximum likelihood estimates are constructed using the em algorithm. The entire analysis is demonstrated in terms of hypothetical data sets.
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