Measurement error models constitute a wide class of models that include linear and nonlinear regression models. They are very useful to model many real-life phenomena, particularly in the medical and biological areas....
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Measurement error models constitute a wide class of models that include linear and nonlinear regression models. They are very useful to model many real-life phenomena, particularly in the medical and biological areas. The great advantage of these models is that, in some sense, they can be represented as mixed effects models, allowing us to implement wellknown techniques, like the em-algorithm for the parameter estimation. In this paper, we consider a class of multivariate measurement error models where the observed response and/or covariate are not fully observed, i.e., the observations are subject to certain threshold values below or above which the measurements are not quantifiable. Consequently, these observations are considered censored. We assume a Student-t distribution for the unobserved true values of the mismeasured covariate and the error term of the model, providing a robust alternative for parameter estimation. Our approach relies on a likelihood-based inference using an em-type algorithm. The proposed method is illustrated through some simulation studies and the analysis of an AIDS clinical trial dataset.
Complex interactions between entities are often represented as edges in a network. In practice, the network is often constructed from noisy measurements and inevitably contains some errors. In this paper we consider t...
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Complex interactions between entities are often represented as edges in a network. In practice, the network is often constructed from noisy measurements and inevitably contains some errors. In this paper we consider the problem of estimating a network from multiple noisy observations where edges of the original network are recorded with both false positives and false negatives. This problem is motivated by neuroimaging applications where brain networks of a group of patients with a particular brain condition could be viewed as noisy versions of an unobserved true network corresponding to the disease. The key to optimally leveraging these multiple observations is to take advantage of network structure, and here we focus on the case where the true network contains communities. Communities are common in real networks in general and in particular are believed to be presented in brain networks. Under a community structure assumption on the truth, we derive an efficient method to estimate the noise levels and the original network, with theoretical guarantees on the convergence of our estimates. We show on synthetic networks that the performance of our method is close to an oracle method using the true parameter values, and apply our method to fMRI brain data, demonstrating that it constructs stable and plausible estimates of the population network.
In the current paper, based on progressive type-II hybrid censored samples, the maximum likelihood and Bayes estimates for the two parameter Burr XII distribution are obtained. We propose the use of expectation-maximi...
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In the current paper, based on progressive type-II hybrid censored samples, the maximum likelihood and Bayes estimates for the two parameter Burr XII distribution are obtained. We propose the use of expectation-maximization (em) algorithm to compute the maximum likelihood estimates (MLEs) of model parameters. Further, we derive the asymptotic variance-covariance matrix of the MLEs by applying the missing information principle and it can be utilized to construct asymptotic confidence intervals (CIs) for the parameters. The Bayes estimates of the unknown parameters are obtained under the assumption of gamma priors by using Lindley's approximation and Markov chain Monte Carlo (MCMC) technique. Also, MCMC samples are used to construct the highest posterior density (HPD) credible intervals. Simulation study is conducted to investigate the accuracy of the estimates and compare the performance of CIs obtained. Finally, one real data set is analyzed for illustrative purposes.
In this paper we show that a recently developed method for the study of ''cultural'' differences, called DBS-em, or Distance Between Strata estimated with the em (Expectation Maximization) algorithm, c...
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In this paper we show that a recently developed method for the study of ''cultural'' differences, called DBS-em, or Distance Between Strata estimated with the em (Expectation Maximization) algorithm, can also be used to circumvent the difficulties posed by APC (or Age, Period, Cohort) models. The DBS-em method produces an original measure of the distance (dependent variable) between any two subsets of observations (strata) within a sample, where the stratification variables can be interpreted as regressors. When these stratification variables are age, period, and cohort, what results is an APC model which, however, proves immune to the ''intrinsic collinearity problem'' (C = P-A). With a few limitations, to be sure, which are discussed in the article. In our application to Italian data over the years 1993-2013, age and cohort strongly shape cultural consumption, while cohort and period impact, but only up to a point, on political participation.
This paper discusses regression analysis of current status data, a type of failure time data where each study subject is observed only once, in the presence of dependent censoring. Furthermore, there may exist a cured...
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This paper discusses regression analysis of current status data, a type of failure time data where each study subject is observed only once, in the presence of dependent censoring. Furthermore, there may exist a cured subgroup, meaning that a proportion of study subjects are not susceptible to the failure event of interest. For the problem, we develop a sieve maximum likelihood estimation approach with the use of latent variables and Bernstein polynomials. For the determination of the proposed estimators, an em algorithm is developed and the asymptotic properties of the estimators are established. Extensive simulation studies are conducted and indicate that the proposed method works well for practical situations. A motivating application from a tumorigenicity experiment is also provided.
Finite mixture regression models have been widely used for modelling mixed regression relationships arising from a clustered and thus heterogenous population. The classical normal mixture model, despite its simplicity...
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Finite mixture regression models have been widely used for modelling mixed regression relationships arising from a clustered and thus heterogenous population. The classical normal mixture model, despite its simplicity and wide applicability, may fail in the presence of severe outliers. Using a sparse, case-specific, and scale-dependent mean-shift mixture model parameterization, we propose a robust mixture regression approach for simultaneously conducting outlier detection and robust parameter estimation. A penalized likelihood approach is adopted to induce sparsity among the mean-shift parameters so that the outliers are distinguished from the remainder of the data, and a generalized Expectation-Maximization (em) algorithm is developed to perform stable and efficient computation. The proposed approach is shown to have strong connections with other robust methods including the trimmed likelihood method and M-estimation approaches. In contrast to several existing methods, the proposed methods show outstanding performance in our simulation studies. (C) 2016 Statistical Society of Canada
In this paper, we propose a penalized likelihood method to simultaneous select covariate, and mixing component and obtain parameter estimation in the localized mixture of experts models. We develop an expectation maxi...
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In this paper, we propose a penalized likelihood method to simultaneous select covariate, and mixing component and obtain parameter estimation in the localized mixture of experts models. We develop an expectation maximization algorithm to solve the proposed penalized likelihood procedure, and introduce a data-driven procedure to select the tuning parameters. Extensive numerical studies are carried out to compare the finite sample performances of our proposed method and other existing methods. Finally, we apply the proposed methodology to analyze the Boston housing price data set and the baseball salaries data set.
Diagnostic classification models are confirmatory in the sense that the relationship between the latent attributes and responses to items is specified or parameterized. Such models are readily interpretable with each ...
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Diagnostic classification models are confirmatory in the sense that the relationship between the latent attributes and responses to items is specified or parameterized. Such models are readily interpretable with each component of the model usually having a practical meaning. However, parameterized diagnostic classification models are sometimes too simple to capture all the data patterns, resulting in significant model lack of fit. In this paper, we attempt to obtain a compromise between interpretability and goodness of fit by regularizing a latent class model. Our approach starts with minimal assumptions on the data structure, followed by suitable regularization to reduce complexity, so that readily interpretable, yet flexible model is obtained. An expectation-maximization-type algorithm is developed for efficient computation. It is shown that the proposed approach enjoys good theoretical properties. Results from simulation studies and a real application are presented.
Missing covariates data is a common issue in generalized linear models (GLMs). A model-based procedure arising from properly specifying joint models for both the partially observed covariates and the corresponding mis...
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Missing covariates data is a common issue in generalized linear models (GLMs). A model-based procedure arising from properly specifying joint models for both the partially observed covariates and the corresponding missing indicator variables represents a sound and flexible methodology, which lends itself to maximum likelihood estimation as the likelihood function is available in computable form. In this paper, a novel model-based methodology is proposed for the regression analysis of GLMs when the partially observed covariates are categorical. Pair-copula constructions are used as graphical tools in order to facilitate the specification of the high-dimensional probability distributions of the underlying missingness components. The model parameters are estimated by maximizing the weighted loglikelihood function by using an em algorithm. In order to compare the performance of the proposed methodology with other well-established approaches, which include complete-cases and multiple imputation, several simulation experiments of Binomial, Poisson and Normal regressions are carried out under both missing at random and non-missing at random mechanisms scenarios. The methods are illustrated by modeling data from a stage III melanoma clinical trial. The results show that the methodology is rather robust and flexible, representing a competitive alternative to traditional techniques.
Two dice are rolled repeatedly, only their sum is registered. Have the two dice been "shaved," so two of the six sides appear more frequently? Pavlides and Perlman discussed this somewhat complicated type of...
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Two dice are rolled repeatedly, only their sum is registered. Have the two dice been "shaved," so two of the six sides appear more frequently? Pavlides and Perlman discussed this somewhat complicated type of situation through curved exponential families. Here, we contrast their approach by regarding data as incomplete data from a simple exponential family. The latter, supplementary approach is in some respects simpler, it provides additional insight about the relationships among the likelihood equation, the Fisher information, and the em algorithm, and it illustrates the information content in ancillary statistics.
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