ECM Algorithm Research Articles

On the Extended Birnbaum–Saunders Distribution Based on the Skew-t-Normal Distribution

In this article, a generalized version of the univariate Birnbaum–Saunders distribution based on the skew-t-normal distribution is introduced and its characterizations, properties are studied. Maximum likelihood estimation of the parameters via the ECM algorithm evaluated by Monte Carlo simulations is also discussed. Finally, two real datasets are analyzed for illustrative purposes.

Distributed ECM Algorithm for OTHR Multipath Target Tracking With Unknown Ionospheric Heights

Over-the-horizon radar (OTHR) target tracking in the presence of complicated ionospheric environment mainly faces three challenges, i.e., discrete uncertainty of multipath data association, continuous uncertainty of ionospheric heights, and coupling of target state estimation and ionospheric parameters identification. The existing OTHR target tracking algorithms demanded that the ionospheric heights should be exactly known or statistical properties known. However, the ionospheric heights is inaccurate due to the inherent variability of ionosphere, especially when the deployment of ionosondes is unavailable in the sea area or hostile zone. This paper introduces a joint optimization scheme called distributed expectation-conditional maximization (DECM), which solves the target state estimation, multipath data association, and ionospheric heights identification simultaneously. The proposed DECM algorithm consists of a local estimation level and a global fusion level, whereas information is exchanged within these two levels until iteration terminates. This dual-level processing framework transforms the high-dimensional estimation problems into several low-dimensional parallel path-dependent estimation problems, which improves the computational efficiency of expectation maximization under high-dimensional latent variables case. In addition, the closed-loop structure is beneficial to the coupling problem. The simulation indicates the effectiveness of the proposed scheme.

Quasi maximum likelihood estimation of dynamic panel data models

ABSTRACTThis article establishes the almost sure convergence and asymptotic normality of levels and differenced quasi maximum likelihood (QML) estimators of dynamic panel data models. The QML estimators are robust with respect to initial conditions, conditional and time-series heteroskedasticity, and misspecification of the log-likelihood. The article also provides an ECME algorithm for calculating levels QML estimates. Finally, it compares the finite-sample performance of levels and differenced QML estimators, the differenced generalized method of moments (GMM) estimator, and the system GMM estimator. The QML estimators usually have smaller— typically substantially smaller—bias and root mean squared errors than the panel data GMM estimators.

Likelihood-based risk estimation for variance-gamma models

Although the variance-gamma distribution is a flexible model for log-returns of financial assets, so far it has found rather limited applications in finance and risk management. One of the reasons is that maximum likelihood estimation of its parameters is not straightforward. We develop an EM-type algorithm based on Nitithumbundit and Chan (An ECM algorithm for skewed multivariate variance gamma distribution in normal mean–variance representation, arXiv:1504.01239 , 2015) that bypasses the evaluation of the full likelihood, which may be difficult because the density is not in closed form and is unbounded for small values of the shape parameter. Moreover, we study the relative efficiency of our approach with respect to the maximum likelihood estimation procedures implemented in the VarianceGamma and ghyp R packages. Extensive simulation experiments and real-data analyses suggest that the multicycle ECM algorithm gives the best results in terms of root-mean-squared-error, for both parameter and value-at-risk estimation. The performance of the routines in the ghyp R package is similar but not as good, whereas the VarianceGamma package produces worse results, especially when the shape parameter is small.

Maximum likelihood estimation in vector autoregressive models with multivariate scaled t-distributed innovations using EM-based algorithms

ABSTRACTThis article is concerned with the likelihood-based inference of vector autoregressive models with multivariate scaled t-distributed innovations by applying the EM-based (ECM and ECME) algorithms. The ECM and ECME algorithms, which are analytically quite simple to use, are applied to find the maximum likelihood estimates of the model parameters and then compared based on the computational running time and the accuracy of estimation via a simulation study. The results demonstrate that the ECME is efficient and usable in practice. We also show how the method can be applied to a multivariate dataset.

EM algorithm for symmetric stable mixture model

ABSTRACTMixture models are frequently used for modeling complex data. An extension of the EM algorithm, here called ECME, is proposed to compute the maximum likelihood estimate of parameters of symmetric -stable mixture model (SSMM). Comprehensive simulation studies are performed to show the performance of the proposed ECME algorithm. The robustness of the SSMM is investigated by simulations when it is used to model data generated from mixture of exponential power and t distributions. Both proposed ECME and Bayesian approaches are applied to three sets of real data, which shows that the proposed ECME algorithm outperforms the Bayesian paradigm for all three sets. Also, the SSMM is compared with the mixture of normal, skew normal, t, and skew t distributions for modeling four sets of real data. It turns out that the SSMM works as well as or better than above models. This can be considered as SSMM capability in robust mixture modeling.

Degradation Data-Driven Remaining Useful Life Estimation in the Absence of Prior Degradation Knowledge

Recent developments in prognostic and health management have been targeted at utilizing the observed degradation signals to estimate residual life distributions. Current degradation models mainly focus on a population of “identical” devices or an individual device with population information, not a single component in the absence of prior degradation knowledge. However, the fast development of science and technology provides us with many kinds of new systems, and we just have the real-time monitoring information to analyze the reliability for them. The fusion algorithm presented herein addresses this challenge by combining the excellent modeling ability of Bayesian updating method for the multilevel data and the prominent estimation ability of ECM algorithm for incomplete data. Residual life distributions and posterior distributions are first calculated through the Bayesian updating method based on random initial a priori distributions. Then the a priori distributions are revised and improved for future predictions by the ECM algorithm. Once a new signal is observed, we can reuse the fusion algorithm to improve the accuracy of residual life distributions. The applicability of this fusion algorithm is validated by a set of simulation experiments.

An empirical Bayes method for genotyping and SNP detection using multi-sample next-generation sequencing data.

The development of next generation sequencing technology provides an efficient and powerful approach to rare variant detection. To identify genetic variations, the essential question is how to quantity the sequencing error rate in the data. Because of the advantage of easy implementation and the ability to integrate data from different sources, the empirical Bayes method is popularly employed to estimate the sequencing error rate for SNP detection. We propose a novel statistical model to fit the observed non-reference allele frequency data, and utilize the empirical Bayes method for both genotyping and SNP detection, where an ECM algorithm is implemented to estimate the model parameters. The performance of our proposed method is investigated via simulations and real data analysis. It is shown that our method makes less genotype-call errors, and with the parameter estimates from the ECM algorithm, it attains high detection power with FDR being well controlled. The proposed algorithm is wrapped in the R package ebGenotyping, which can be downloaded from http://cran.r-project.org/web/packages/ebGenotyping/ CONTACT: youn@mail.sysu.edu.cnSupplementary information: Supplementary data are available at Bioinformatics online.

Skewed factor models using selection mechanisms

Traditional factor models explicitly or implicitly assume that the factors follow a multivariate normal distribution; that is, only moments up to order two are involved. However, it may happen in real data problems that the first two moments cannot explain the factors. Based on this motivation, here we devise three new skewed factor models, the skew-normal, the skew- t , and the generalized skew-normal factor models depending on a selection mechanism on the factors. The ECME algorithms are adopted to estimate related parameters for statistical inference. Monte Carlo simulations validate our new models and we demonstrate the need for skewed factor models using the classic open/closed book exam scores dataset.

Extending mixtures of factor models using the restricted multivariate skew-normal distribution

The mixture of factor analyzers (MFA) model provides a powerful tool for analyzing high-dimensional data as it can reduce the number of free parameters through its factor-analytic representation of the component covariance matrices. This paper extends the MFA model to incorporate a restricted version of the multivariate skew-normal distribution to model the distribution of the latent component factors, called mixtures of skew-normal factor analyzers (MSNFA). The proposed MSNFA model allows us to relax the need for the normality assumption for the latent factors in order to accommodate skewness in the observed data. The MSNFA model thus provides an approach to model-based density estimation and clustering of high-dimensional data exhibiting asymmetric characteristics. A computationally feasible ECM algorithm is developed for computing the maximum likelihood estimates of the parameters. Model selection can be made on the basis of three commonly used information-based criteria. The potential of the proposed methodology is exemplified through applications to two real examples, and the results are compared with those obtained from fitting the MFA model.

Automatic Modulation Classification for Low SNR Digital Signal in Frequency-Selective Fading Environments

In this research, a classifier is proposed for automatic modulation classification of some common modulation schemes, i.e., BPSK, QPSK, 8-PSK and 16-QAM. Our proposed classifier considers multipath fading effects on the received signal in a non-Gaussian noise environment. Automatic modulation classification is very challenging in real-world scenarios due to fading effects and additive Gaussian mixture noise on modulation schemes. Most of the available modulation classifiers do not consider the fading effects which results in degradation of classification in a blind channel environment. In our work, the channel is supposed to be suffering from excessive additive Gaussian mixture noise and frequency selective fading resulting in low signal SNR. The estimation of the unknown channel along with noise parameters is performed using ECM algorithm and then used in maximum-likelihood classifier for the classification of modulation schemes. Simulation results are presented that show 2 dB improvement in performance than classifier which considers only Gaussian noise in the received signal.

Linear mixed function-on-function regression models.

We develop a linear mixed regression model where both the response and the predictor are functions. Model parameters are estimated by maximizing the log likelihood via the ECME algorithm. The estimated variance parameters or covariance matrices are shown to be positive or positive definite at each iteration. In simulation studies, the approach outperforms in terms of the fitting error and the MSE of estimating the "regression coefficients."

Modeling Sustained Treatment Effects in Tumor Xenograft Experiments

In cancer drug development, demonstrated efficacy in tumor xenograft models is an important step toward bringing a promising compound to human use. A key outcome variable is tumor volume measured over a period of time, while mice are treated with certain treatment regimens. A constrained parametric model has been proposed to account for special features, such as intrinsic tumor growth, or tumor volume truncations due to tumor size being either too large or too small to detect. However, since the drug concentration in the blood of a mouse or its tissues may be stabilized at a certain level and maintained during a period of time, the treatment may have sustained effects. This article extends the constrained parametric model to account for the sustained drug effects. The ECM algorithm for incomplete data is applied to estimating the dose-response relationship in the proposed model. The model selection based on likelihood functions is given and a simulation study is conducted to investigate the performance of the proposed estimator. A real xenograft study on the antitumor agent temozolomide combined with irinotecan against the rhabdomyosarcoma is analyzed using the proposed methods.

Likelihood-Based Inference in Autoregressive Models with Scaled t-Distributed Innovations by Means of EM-Based Algorithms

This article applies the EM-based (ECM and ECME) algorithms to find the maximum likelihood estimates of model parameters in general AR models with independent scaled t-distributed innovations whenever the degrees of freedom are unknown. The ECME, sharing advantages with both EM and Newton–Raphson algorithms, is an extension of ECM, which itself is an extension of the EM algorithm. The ECM and ECME algorithms, which are analytically quite simple to use, are then compared based on the computational running time and the accuracy of estimation via a simulation study. The results demonstrate that the ECME is efficient and usable in practice. We also show how our method can be applied to the Wolfer's sunspot data.

An accumulator model for responses and response times in tests based on the proportional hazards model

Latent trait models for responses and response times in tests often lack a substantial interpretation in terms of a cognitive process model. This is a drawback because process models are helpful in clarifying the meaning of the latent traits. In the present paper, a new model for responses and response times in tests is presented. The model is based on the proportional hazards model for competing risks. Two processes are assumed, one reflecting the increase in knowledge and the second the tendency to discontinue. The processes can be characterized by two proportional hazards models whose baseline hazard functions correspond to the temporary increase in knowledge and discouragement. The model can be calibrated with marginal maximum likelihood estimation and an application of the ECM algorithm. Two tests of model fit are proposed. The amenability of the proposed approaches to model calibration and model evaluation is demonstrated in a simulation study. Finally, the model is used for the analysis of two empirical data sets.

The application of Quasi-Newton ECM algorithm to MUD

The application of Quasi-Newton ECM algorithm to MUD

The Application of Quasi-Newton ECME Algorithm to MUD

The Application of Quasi-Newton ECME Algorithm to MUD

Likelihood Based Inference Mixed-Effects Models with Censored Responses Using the Multivariate-t Distribution

Mixed-effects models are commonly used to fit longitudinal or repeated measures data. A complication arises when the response is censored, for example, due to limits of quantification of the assay used. Although normal distributions are commonly assumed for random effects and residual errors, such assumptions make inferences vulnerable to outliers. The sensitivity to outliers and the need for heavy tailed distributions for random effects and residual errors motivate us to develop a likelihood-based inference for linear and nonlinear mixed effects models with cen- sored response (NLMEC/LMEC) based on the multivariate Student-t distribution. An ECM algorithm is developed for computing the maximum likelihood estimates for NLMEC/LMEC with the standard errors of the fixed effects and the exact like- lihood value as a by-product. The algorithm uses closed-form expressions at the E-step, that rely on formulas for the mean and variance of a truncated multivariate- t distribution. The proposed algorithm is implemented in the R package tlmec. It is applied to analyze longitudinal HIV viral load data in two recent AIDS studies. In addition, a simulation study is conducted to examine the performance of the proposed method and to compare it with the approach of Vaida and Liu (2009).

An ECM Estimation Approach for Analyzing Multivariate Skew-Normal Data with Dropout

In this article, an ECM algorithm is developed to obtain the maximum likelihood estimates of parameters where multivariate skew-normal distribution is used for analyzing longitudinal skewed normal regression data with dropout. A simulation study is performed to investigate the performance of the presented algorithm. Also, the methodology is illustrated through two applications and the results of proposed methodology are compared with ECM under multivariate normal assumption using AIC and BIC criteria. Standard errors of parameter estimates are obtained by asymptotic observed information matrix.

On Computing Maximum-Likelihood Estimates of the Unbalanced Two-Way Random-Effects Model

This article applies the ECME algorithm to derive an easily implemented iterative feasible generalized least squares procedure for calculating maximum-likelihood estimates of the parameters of the unbalanced two-way random-effects model. The algorithm increases the log-likelihood monotonically and the fitted variance components are guaranteed to be non negative. This article applies the algorithm in an example.