We consider a new recursive algorithm for parameter estimation from an independent incomplete data sequence. The algorithm can be viewed as a recursive version of the well-known em algorithm, augmented with a Monte-Ca...
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We consider a new recursive algorithm for parameter estimation from an independent incomplete data sequence. The algorithm can be viewed as a recursive version of the well-known em algorithm, augmented with a Monte-Carlo step which restores the missing data. Based on recent results on stochastic algorithms, we give conditions for the a.s. convergence of the algorithm. Moreover, asymptotical variance of this estimator is reduced by a simple averaging. Application to finite mixtures is given with a simulation experiment.
Information derived from interim sacrifices or on cause of death is routinely used in the statistical analyses of carcinogenicity experiments involving occult tumours. The authors describe a simple semiparametric mode...
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Information derived from interim sacrifices or on cause of death is routinely used in the statistical analyses of carcinogenicity experiments involving occult tumours. The authors describe a simple semiparametric model which does not require this information. Natural deaths during the experiment and the usual terminal sacrifice provide sufficient information to ensure that the tumour incidence rates, which are of primary interest in occult-tumour studies, can be estimated nonparametrically. The advantages of this semiparametric approach to the analysis of survival/sacrifice experiments are illustrated using data from a study on benzyl acetate conducted under the U. S. National Toxicology Program. The results derived compare favourably with those obtained using a previously published approach to the analysis of tumorigenicity data.
In this paper we present a logistic mixture model for rain rate, that is, a model where the regime probabilities are allowed to change over time and are modeled with a logistic regression structure. Such a model may b...
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Suppose that some components are initially operated in a certain condition and then switched to operating in a different condition. Working hours of the components in condition 1 and condition 2 are respectively obser...
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We propose a smooth hazard estimator for interval-censored survival data using the method of local likelihood. The model is fit using a local em algorithm. The estimator is more descriptive than traditional empirical ...
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We propose a smooth hazard estimator for interval-censored survival data using the method of local likelihood. The model is fit using a local em algorithm. The estimator is more descriptive than traditional empirical estimates in regions of concentrated information and takes on a parametric flavor in regions of sparse information. We derive two different standard error estimates for the smooth curve, one based on asymptotic theory and the other on the bootstrap. We illustrate the local em method for times to breast cosmesis deterioration (Finkelstein, 1986, Biometrics 42, 845-854) and for times to HIV-1 infection for individuals with hemophilia (Kroner et al., 1994, Journal of AIDS 7, 279-286). Our hazard estimates for each of these data sets show interesting structures that would not be found using a standard parametric hazard model or empirical survivorship estimates.
We propose a method for estimating parameters for general parametric regression models with an arbitrary number of missing covariates. We allow any pattern of missing data and assume that the missing data mechanism is...
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We propose a method for estimating parameters for general parametric regression models with an arbitrary number of missing covariates. We allow any pattern of missing data and assume that the missing data mechanism is ignorable throughout. When the missing covariates are categorical, a useful technique for obtaining parameter estimates is the em algorithm by the method of weights proposed in Ibrahim (1990, Journal of the American Statistical Association 85, 765-769). We extend this method to continuous or mixed categorical and continuous covariates, and for arbitrary parametric regression models, by adapting a Monte Carlo version of the em algorithm as discussed by Wei and Tanner (1990, Journal of the American, Statistical Association 85, 699-704). In addition, we discuss the Gibbs sampler for sampling from the conditional distribution of the missing covariates given the observed data and show that the appropriate complete conditionals are log-concave. The log-concavity property of the conditional distributions will facilitate a straightforward implementation of the Gibbs sampler via the adaptive rejection algorithm of Gilks and Wild (1992, Applied Statistics 41, 337-348). We assume the model for the response given the covariates is an arbitrary parametric regression model, such as a generalized linear model, a parametric survival model, or a nonlinear model. We model the marginal distribution of the covariates as a product of one-dimensional conditional distributions. This allows us a great deal of flexibility in modeling the distribution of the covariates and reduces the number of nuisance parameters that are introduced in the E-step. We present examples involving both simulated and real data.
In this paper, the constrained maximum likelihood estimation of a two-level covariance structure model with unbalanced designs is considered. The two-level model is reformulated as a single-level model by treating the...
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In this paper, the constrained maximum likelihood estimation of a two-level covariance structure model with unbalanced designs is considered. The two-level model is reformulated as a single-level model by treating the group level latent random Vectors as hypothetical missing-data. Then, the popular em algorithm is extended to obtain the constrained maximum likelihood estimates. For general nonlinear constraints, the multiplier method is used at the M-step to find the constrained minimum of the conditional expectation. An accelerated em gradient procedure is derived to handle linear constraints. The empirical performance of the proposed em type algorithms is illustrated by some artifical and real examples.
A method of computing the observed information for the hidden Markov model using the em algorithm and the results of Louis (1982) is described. Generating the ''exact'' information may be computational...
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A method of computing the observed information for the hidden Markov model using the em algorithm and the results of Louis (1982) is described. Generating the ''exact'' information may be computationally intensive for large datasets but an approximation is given which significantly reduces the computational effort in most cases.
This paper shows how multiple shape hypotheses can be used to recognise complex line patterns using the expectation-maximisation algorithm. The idea underpinning this work is to construct a mixture distribution for an...
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This paper shows how multiple shape hypotheses can be used to recognise complex line patterns using the expectation-maximisation algorithm. The idea underpinning this work is to construct a mixture distribution for an observed configuration of line segments over a space of hypothesised shape models. According to the em framework each model is represented by a set of maximum likelihood registration parameters together with a set of matching probabilities. These two pieces of information are iteratively updated so as to maximise the expected data likelihood over the space of model-data associations. This architecture can be viewed as providing simultaneous shape registration and hypothesis verification. We illustrate the effectiveness of the recognition strategy by studying the registration of noisy radar data against a database of alternative cartographic maps for different locations. (C) 1997 Elsevier Science B.V.
This paper describes an application of the em (expectation and maximisation) algorithm to the registration of incomplete millimetric radar images. The data used in this study consists of a series of non-overlapping ra...
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This paper describes an application of the em (expectation and maximisation) algorithm to the registration of incomplete millimetric radar images. The data used in this study consists of a series of non-overlapping radar sweeps. Our registration process aims to recover transformation parameters between the radar-data and a digital map. The tokens used in the matching process are fragmented line-segments extracted from the radar images which predominantly correspond to hedge-rows in the cartographic data. The em technique models data uncertainty using Gaussian mixtures defined over the positions and orientations of the lines. The resulting weighted least-squares parameter estimation problem is solved using the Levenberg-Marquardt method. A sensitivity analysis reveals that the data-likelihood function is unimodal in the translation and scale parameters. In fact, the algorithm is only potentially sensitive to the choice of initial rotation parameter;this is attributable to local sub-optima in the log-likelihood function associated with pi/2 orientation ambiguities in the map. By adopting Levenberg-Marquardt optimisation we reduce the local convergence difficulties posed by these local rotation maxima. The method is also demonstrated to be relatively insensitive to random measurement errors on the line-segments. (C) 1997 Elsevier Science B.V.
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