Multidimensional discrete-parameter processes with factorable covariance structure are of great importance for applications and approximations to certain continuous-parameter processes. In practical situations, usuall...
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Multidimensional discrete-parameter processes with factorable covariance structure are of great importance for applications and approximations to certain continuous-parameter processes. In practical situations, usually only incomplete data are available, so state-space schemes are normally used for modelling and prediction. In this work we describe maximum-likelihood estimation and smoothing for doubly geometric lattice processes using incomplete data. The procedure proposed is based on an application of the em algorithm, and is inspired by its use in time-series analysis. Minimum mean-square-error prediction is also described. Extension to more general models is commented on. Some examples using simulated data are provided.
We address the problem of providing variances for parameter estimates obtained under a penalized likelihood formulation through use of the em algorithm. The solution proposed represents a synthesis of two existent tec...
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We address the problem of providing variances for parameter estimates obtained under a penalized likelihood formulation through use of the em algorithm. The solution proposed represents a synthesis of two existent techniques. Firstly, we exploit the supplemented em algorithm developed by Meng and Rubin that provides variance estimates for maximum likelihood estimates obtained via the em algorithm. Their procedure relies on evaluating the Jacobian of the mapping induced by the em algorithm. Secondly, we utilize results from Green that provide expressions for Jacobians of mappings induced by em algorithms applied to a penalized likelihood. The resultant procedure requires no more code than that needed for the penalized em algorithm itself. The technique is demonstrated with an illustrative example.
In this paper we derive a recursive em algorithm for identification of ARX-models in the case of missing data. Convergence analysis using the ODE approach is indicated. The algorithm is tested via Monte-Carlo simulati...
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In this paper we derive a recursive em algorithm for identification of ARX-models in the case of missing data. Convergence analysis using the ODE approach is indicated. The algorithm is tested via Monte-Carlo simulation and compared to other approaches.
Extensions of the Cox proportional hazards model for survival data are studied where allowance is made for unobserved heterogeneity and for correlation between the life times of several individuals. The extended model...
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Extensions of the Cox proportional hazards model for survival data are studied where allowance is made for unobserved heterogeneity and for correlation between the life times of several individuals. The extended models are frailty models inspired by YASHIN et al. (1995). Estimation is carried out using the em algorithm. Inference is discussed and potential applications are outlined, in particular to statistical research in human genetics using twin data or adoption data, aimed at separating the effects of genetic and environmental factors on mortality.
In the stochastic volatility framework of Hull and White (1987), we characterize the so-called Black and Scholes implied volatility as a function of two arguments: the ratio of the strike to the underlying asset price...
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In the stochastic volatility framework of Hull and White (1987), we characterize the so-called Black and Scholes implied volatility as a function of two arguments: the ratio of the strike to the underlying asset price and the instantaneous value of the volatility. By studying the variations in the first argument, we show that the usual hedging methods, through the Black and Scholes model, lead to an underhedged (resp. overhedged) position for in-the-money (resp. out-of-the-money) options, and a perfect partial hedged position for at-the-money options. These results are shown to be closely related to the smile effect, which is proved to be a natural consequence of the stochastic volatility feature. The deterministic dependence of the implied volatility on the underlying volatility process suggests the use of implied volatility data for the estimation of the parameters of interest. A statistical procedure of filtering (of the latent volatility process) and estimation (of its parameters) is shown to be strongly consistent and asymptotically normal.
This paper presents an easy-to-compute semi-parametric (SP) method to estimate a simple disequilibrium model proposed by Fair and Jaffee (1972). The proposed approach is based on a non-parametric interpretation of the...
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To realize an input-output relation given by noise-contaminated examples, it is effective to use a stochastic model of neural networks. When the model network includes hidden units whose activation values are not spec...
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To realize an input-output relation given by noise-contaminated examples, it is effective to use a stochastic model of neural networks. When the model network includes hidden units whose activation values are not specified nor observed, it is useful to estimate the hidden variables from the observed or specified input-output data based on the stochastic model. Two algorithms, the em and em algorithms, have so far been proposed for this purpose. The em algorithm is an iterative statistical technique of using the conditional expectation, and the em algorithm is a geometrical one given by information geometry. The em algorithm minimizes iteratively the Kullback-Leibler divergence in the manifold of neural networks. These two algorithms are equivalent in most cases. The present paper gives a unified information geometrical framework for studying stochastic models of neural networks, by focusing on the em and em algorithms, and proves a condition that guarantees their equivalence. Examples include: (1) stochastic multilayer perceptron, (2) mixtures of experts, and (3) normal mixture model.
The Expectation-Maximization (em) algorithm is an iterative approach to maximum likelihood parameter estimation. Jordan and Jacobs recently proposed an em algorithm for the mixture of experts architecture of Jacobs, J...
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The Expectation-Maximization (em) algorithm is an iterative approach to maximum likelihood parameter estimation. Jordan and Jacobs recently proposed an em algorithm for the mixture of experts architecture of Jacobs, Jordan, Nowlan and Hinton (1991) and the hierarchical mixture of experts architecture of Jordan and Jacobs (1992). They showed empirically that the em algorithm for these architectures yields significantly faster convergence than gradient ascent. In the current paper we provide a theoretical analysis of this algorithm. We show that the algorithm can be regarded as a variable metric algorithm with its searching direction having a positive projection on the gradient of the log likelihood. We also analyze the convergence of the algorithm and provide an explicit expression for the convergence rate. In addition, we describe an acceleration technique that yields a significant speedup in simulation experiments.
This paper considers the estimation of signal parameters and their enhancement using an approach based on the estimation-maximation (em) algorithm, when only noisy observation data are available. The algorithm is deri...
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This paper considers the estimation of signal parameters and their enhancement using an approach based on the estimation-maximation (em) algorithm, when only noisy observation data are available. The algorithm is derived with an application to speech signals. The distribution of the excitation source for the speech signal is assumed as a mixture of two Gaussian probability distribution functions with differing variances. This mixture assumption is experimentally valid in enhancing noise-corrupted speech, We recursively estimate the signal parameters and analyze the characteristics of its excitation source in a sequential manner. In the maximum likelihood estimation scheme we utilize the em algorithm, and employ a detection and an estimation step for the parameters. For their enhancement we use a Kalman filter for the parameters obtained from the estimation procedure, Simulation results using synthetic and real speech data confirm the improved performance of our algorithm in noisy situations, with an increase of about 3 dB in terms of output SNR compared to conventional Gaussian assumption. The proposed algorithm also may be noteworthy in that it needs no voiced/unvoiced decision logic, thanks to the use of the residual approach in the speech signal model.
A locally optimal detection algorithm for random signals in dependent noise is derived and applied to independent identically distributed complex-valued Gaussian mixture noise, The resulting detector is essentially a ...
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A locally optimal detection algorithm for random signals in dependent noise is derived and applied to independent identically distributed complex-valued Gaussian mixture noise, The resulting detector is essentially a weighted sum of pow-er detectors-the power detector is the locally optimal detector for random signals in Gaussian noise, The weighting functions are modified to enhance the detection performance for small sample sizes, An implementation of the mixture detector, using the expectation-maximization algorithm, is described, Moments of these detectors are calculated from piecewise-polynomial approximations of the weighting functions, The sum of sufficiently many independent identically distributed detector outputs is then approximated by a normal distribution. Probability distributions are also derived for the power detector in Gaussian mixture noise, For a particular set of noise parameters, the theoretical distributions are compared with those obtained from Monte Carlo simulation and seen to be quite dose, The theoretical distributions are then used to compare the performance of the mixture and power detectors in Gaussian mixture noise over a range of parameters and to assess the impact of parameter error on detection performance, In this study, the signal gain of the mixture detectors varies from 15 to 38 dB, and the degradation of the probability of detection due to parameter estimation error is relatively minor.
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