The paper discusses the main ideas of an implementation of em-type algorithms for computing on the graphics processors and the application for the probabilistic models based on the Cox processes. An example of the GPU...
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ISBN:
(纸本)9780735412873
The paper discusses the main ideas of an implementation of em-type algorithms for computing on the graphics processors and the application for the probabilistic models based on the Cox processes. An example of the GPU's adapted MATLAB source code for the finite normal mixtures with the expectation-maximization matrix formulas is given. The testing of computational efficiency for GPU vs CPU is illustrated for the different sample sizes.
In recent years, some interested data can be recorded only if the values fall within an interval range, and the responses are often subject to censoring. Attempting to perform effective statistical analysis with censo...
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In recent years, some interested data can be recorded only if the values fall within an interval range, and the responses are often subject to censoring. Attempting to perform effective statistical analysis with censored, especially heavy-tailed and asymmetric data, can be difficult. In this paper, we develop a novel linear regression model based on the proposed skewed generalized t distribution for censored data. The likelihood-based inference and diagnostic analysis are established using the Expectation/Conditional Maximization Either algorithm in conjunction with smoothing approximate functions. We derive relevant measures to perform global influence for this novel model and develop local influence analysis based on the conditional expectation of the complete-data log-likelihood function. Some useful perturbation schemes are discussed. We illustrate the finite sample performance and the robustness of the proposed method by simulation studies. The proposed model is compared with other procedures based on a real dataset, and a sensitivity analysis is also conducted.
Bounded data on (0, 1) have often been modelled in several real-world applications using several distributions. However, these studies lack addressing skewness, kurtosis and heavy-tailed properties in observations. Th...
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Bounded data on (0, 1) have often been modelled in several real-world applications using several distributions. However, these studies lack addressing skewness, kurtosis and heavy-tailed properties in observations. This study presents a novel skew-normal type distribution defined within a bounded interval, which is derived by integrating the structures of skew-normal distributions and the logit function. With its extended skewness and bounded properties, the proposed model provides a versatile and suitable solution for modeling rates and proportions. We have developed an em-type algorithm to accurately estimate the model parameters and its finite mixtures. To illustrate the effectiveness of our approach, we conducted experiments that included two simulation studies and an analysis of real data. The results highlight the flexibility and accuracy of our proposed model in comparison to traditional mixture models.
A class of skew flexible scale mixtures of normal distributions is proposed as a novel device for modeling asymmetric and bimodal data. Computationally feasible em-type algorithms derived from the selection mechanism ...
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A class of skew flexible scale mixtures of normal distributions is proposed as a novel device for modeling asymmetric and bimodal data. Computationally feasible em-type algorithms derived from the selection mechanism are presented to compute its maximum likelihood (ML) estimates. Some characterizations and probabilistic properties of the proposed distributions are also studied. Monte Carlo simulations show that the proposed estimating procedures can provide desirable asymptotic properties of the ML estimates. The usefulness of the proposed methodology is illustrated by analyzing two real datasets on nickel concentration in a soil degradation study, and cost of living for 576 cities around the world.
Finite mixture models have been widely used to model and analyze data from heterogeneous populations. In practical scenarios, these types of data often confront upper and/or lower detection limits due to the constrain...
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Finite mixture models have been widely used to model and analyze data from heterogeneous populations. In practical scenarios, these types of data often confront upper and/or lower detection limits due to the constraints imposed by experimental apparatuses. Additional complexity arises when measures of each mixture component significantly deviate from the normal distribution, manifesting characteristics such as multimodality, asymmetry, and heavy-tailed behavior, simultaneously. This paper introduces a flexible model tailored for censored data to address these intricacies, leveraging the finite mixture of skew-t distributions. An Expectation Conditional Maximization Either (ECME) algorithm, is developed to efficiently derive parameter estimates by iteratively maximizing the observed data log-likelihood function. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of truncated skew-t distributions. Moreover, a method based on general information principles is presented for approximating the asymptotic covariance matrix of the estimators. Results obtained from the analysis of both simulated and real datasets demonstrate the proposed method's effectiveness.
In the framework of censored regression models, the distribution of the error term can depart significantly from normality, for instance, due to the presence of multimodality, skewness and/or atypical observations. In...
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In the framework of censored regression models, the distribution of the error term can depart significantly from normality, for instance, due to the presence of multimodality, skewness and/or atypical observations. In this paper we propose a novel censored linear regression model where the random errors follow a finite mixture of scale mixtures of normal (SMN) distribution. The SMN is an attractive class of symmetrical heavy-tailed densities that includes the normal, Student-t, slash and the contaminated normal distribution as special cases. This approach allows us to model data with great flexibility, accommodating simultaneously multimodality, heavy tails and skewness depending on the structure of the mixture components. We develop an analytically tractable and efficient em-type algorithm for iteratively computing the maximum likelihood estimates of the parameters, with standard errors and prediction of the censored values as a by-products. The proposed algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated SMN distributions. The efficacy of the method is verified through the analysis of simulated and real datasets. The methodology addressed in this paper is implemented in the R package CensMixReg.
Finite mixture models have been widely used to model and analyze data from a heterogeneous populations. Moreover, data of this kind can be missing or subject to some upper and/or lower detection limits because of the ...
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Finite mixture models have been widely used to model and analyze data from a heterogeneous populations. Moreover, data of this kind can be missing or subject to some upper and/or lower detection limits because of the constraints of experimental apparatuses. Another complication arises when measures of each population depart significantly from normality, such as asymmetric behavior. For such data structures, we propose a robust model for censored and/or missing data based on finite mixtures of multivariate skew-normal distributions. This approach allows us to model data with great flexibility, accommodating multimodality and skewness, simultaneously, depending on the structure of the mixture components. We develop an analytically simple, yet efficient, em-type algorithm for conducting maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of the truncated multivariate skew-normal distributions. Furthermore, a general information-based method for approximating the asymptotic covariance matrix of the estimators is also presented. Results obtained from the analysis of both simulated and real datasets are reported to demonstrate the effectiveness of the proposed method. The proposed algorithm and method are implemented in the new R package CensMFM.
A scale-shape mixtures of flexible generalized skew normal (SSMFGSN) distributions is proposed as a novel device for modeling asymmetric data. Computationally feasible em-type algorithms derived from the selection mec...
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A scale-shape mixtures of flexible generalized skew normal (SSMFGSN) distributions is proposed as a novel device for modeling asymmetric data. Computationally feasible em-type algorithms derived from the selection mechanism are presented to compute maximum likelihood (ML) estimates of SSMFGSN distributions. Some characterizations and probabilistic properties of the SSMFGSN distributions are also studied. Monte Carlo simulations show that the proposed estimating procedures can provide desirable asymptotic properties of the ML estimates and demand less computational burden in comparison with other existing algorithms based on convolution representations. The usefulness of the proposed methodology is illustrated by analyzing a real dataset.
The Heckman selection model is perhaps the most popular econometric model in the analysis of data with sample selection. The analyses of this model are based on the normality assumption for the error terms, however, i...
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The Heckman selection model is perhaps the most popular econometric model in the analysis of data with sample selection. The analyses of this model are based on the normality assumption for the error terms, however, in some applications, the distribution of the error term departs significantly from normality, for instance, in the presence of heavy tails and/or atypical observation. In this paper, we explore the Heckman selection-t model where the random errors follow a bivariate Student's-t distribution. We develop an analytically tractable and efficient em-type algorithm for iteratively computing maximum likelihood estimates of the parameters, with standard errors as a by-product. The algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated Student's-t distributions. Simulation studies show the vulnerability of the Heckman selection-normal model, as well as the robustness aspects of the Heckman selection-t model. Two real examples are analyzed, illustrating the usefulness of the proposed methods. The proposed algorithms and methods are implemented in the new R package Heckmanem. (C) 2021 Elsevier Inc. All rights reserved.
It is now a common knowledge that most data that occur in practice violate the assumption of normality. The Student's t distribution is not only a handy alternative to such a case but also possesses a structure th...
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It is now a common knowledge that most data that occur in practice violate the assumption of normality. The Student's t distribution is not only a handy alternative to such a case but also possesses a structure that makes estimation easy via numerical computation. This paper focuses on maximum-likelihood estimation of the parameters of autoregressive regression model driven by Student's t distribution. em-type algorithms are utilized to iteratively obtain the maximum-likelihood estimates of the parameters of the model. The method's performance is compared with the method of modified maximum-likelihood estimation in simulations and real data analysis.
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