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Using the accelerated failure time model to analyze current status data with misclassified covariates

ELECTRONIC JOURNAL OF STATISTICS 2021年第1期15卷 1372-1394页

作者： Chen, Baojiang Qin, Jing Yuan, Ao Univ Texas Hlth Sci Ctr Houston Dept Biostat & Data Sci Sch Publ Hlth Austin Austin TX 78701 USA NIAID NIH 9000 Rockville Pike Bethesda MD 20892 USA Georgetown Univ Dept Biostat Bioinformat & Biomath Washington DC 20057 USA

Current status data arise commonly in applications when there is only one feasible observation time to check if the failure time has occurred, but the exact failure time remains unknown. To accommodate the covariate effect on failure time, the accelerated failure time (AFT) model has been widely used to analyze current status data with the distribution of the failure time assumed to be specified or unspecified. In this paper, we consider a logistic regression with a misclassfied covariate from the current status observation scheme. A semiparametric AFT model was built to model current status data to eliminate the bias caused by this misclassification. This model is also robust to the misspecification of the failure time compared to the parametric AFT model, as we assume an unknown distribution of the failure time in the proposed model. Furthermore, incorporating the covariate effect on the failure time increases the flexibility of the model. Finally, we adapt the Expectation-Maximization algorithm for estimation, which guarantees the convergence of the estimate. Both theory and empirical studies show the consistency of the estimator.

关键词： AFT current status data em algorithm misclassification pool adjacent violator algorithm (PAVA) semiparametric

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Improvements on scalable stochastic Bayesian inference methods for multivariate Hawkes process

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STATISTICS AND COMPUTING 2024年第2期34卷 85-85页

作者： Jiang, Alex Ziyu Rodriguez, Abel Univ Washington Dept Stat Seattle WA 98195 USA

Multivariate Hawkes Processes (MHPs) are a class of point processes that can account for complex temporal dynamics among event sequences. In this work, we study the accuracy and computational efficiency of three classes of algorithms which, while widely used in the context of Bayesian inference, have rarely been applied in the context of MHPs: stochastic gradient expectation-maximization, stochastic gradient variational inference and stochastic gradient Langevin Monte Carlo. An important contribution of this paper is a novel approximation to the likelihood function that allows us to retain the computational advantages associated with conjugate settings while reducing approximation errors associated with the boundary effects. The comparisons are based on various simulated scenarios as well as an application to the study of risk dynamics in the Standard & Poor's 500 intraday index prices among its 11 sectors.

关键词： Hawkes processes Stochastic optimization Variational inference em algorithm Langevin Monte Carlo Bayesian inference

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Denoising of Low Light Images using Patch Priors and Wavelets

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ENGINEERING LETTERS 2021年第3期29卷 1248-1263页

作者： Kannoth, Sreekala Kumar, Sateesh H. C. Raja, K. B. VTU Sapthagiri Coll Engn Belagavi Bengaluru India VTU Sapthagiri Coll Engn Dept Elect & Commun Engn Belagavi Bengaluru India Univ Visvesvaraya Coll Engn Dept Elect & Commun Engn Bengaluru India

The work aims to find a novel technique to remove noise from low light or low luminous level images to improve the visibility of the image and the performance of many image processing systems. A denoising technique using patch priors in wavelet domain for images with low luminous levels, with the help of the Gaussian Mixture Model, is presented here. The main idea is to perform denoising in a sparse domain. Initially, the image is decomposed into approximate and detailed components with the help of wavelet transform, and then the patch based Gaussian mixture model denoising process is applied on both approximate and detailed components. Expectation maximization algorithm is used for estimating the Gaussian mixture model parameters from the image patches. After denoising each component, inverse wavelet transform is applied to obtain the denoised output image. This denoising method was applied to a set of natural low luminous level images, and it resulted in clean images with good Peak Signal to Noise Ratio and Structural Similarity Index, compared to other conventional methods. This work is a novel method combining wavelet transform and Gaussian mixture model for the denoising of low light images.

关键词： em algorithm GMM Denoising MAP estimation Wavelet decomposition

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Hypotheses tests on the skewness parameter in a multivariate generalized hyperbolic distribution

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BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS 2021年第3期35卷 630-655页

作者： Galea, Manuel Vilca, Filidor Zeller, Camila Borelli Pontificia Univ Catolica Chile Santiago Chile Univ Estadual Campinas Sao Paulo Brazil Univ Fed Juiz Fora Juiz De Fora MG Brazil

The class of generalized hyperbolic (GH) distributions is generated by a mean-variance mixture of a multivariate Gaussian with a generalized inverse Gaussian (GIG) distribution. This rich family of GH distributions includes some well-known heavy-tailed and symmetric multivariate distributions, including the Normal Inverse Gaussian and some members of the family of scale-mixture of skew-normal distributions. The class of GH distributions has received considerable attention in finance and signal processing applications. In this paper, we propose the likelihood ratio (LR) test to test hypotheses about the skewness parameter of a GH distribution. Due to the complexity of the likelihood function, the em algorithm is used to find the maximum likelihood estimates both in the complete model and the reduced model. For comparative purposes and due to its simplicity, we also consider the Gradient (G) test. A simulation study shows that the LR and G tests are usually able to achieve the desired significance levels and the testing power increases as the asymmetry increases. The methodology developed in the paper is applied to two real datasets.

关键词： gradient test em algorithm generalized hyperbolic distribution normal inverse Gaussian distribution Likelihood ratio test

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A new framework for examining creditworthiness of borrowers: the mover-stayer model with covariate and macroeconomic effects

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QUANTITATIVE FINANCE 2021年第9期21卷 1491-1499页

作者： Frydman, Halina Matuszyk, Anna Li, Chang Zhu, Weicheng NYU Dept Technol Operat & Stat Stern Sch Business 44 West 4th St New York NY 10012 USA Warsaw Sch Econ Inst Finance Warsaw Poland Princeton Univ Operat Res & Financial Engn Dept Princeton NJ 08544 USA NYU Courant Inst Math Sci New York NY USA

We develop a novel extension of the mover-stayer model to allow for time-dependent variables such as macroeconomic factors and apply it to the repayment process for car loans. The MS model postulates a simple form of population heterogeneity, which is particularly well suited to describing the repayment process: a proportion of borrowers always repay on time (stayers), and a complementary proportion evolves according to a discrete-time Markov chain (movers), with an absorbing default state. In contrast to the literatures focus on the determinants of defaults, our extension examines the determinants of creditworthy borrowers (stayers). We model the probability of borrowers being stayers as a logistic function of their time-fixed covariates as well as of macroeconomic variables. The car-loans data set, obtained from a Polish bank, contains a large number of characteristics for each borrower and their repayment histories. The MS models' estimation from these data indicates that annual GDP growth is the only macroeconomic variable exerting a substantial effect on the stayers' probability: as GDP increases, so does the proportion of stayers. Because stayers are the most desirable borrowers, the proposed model should be useful to institutional lenders.

关键词： Mover-stayer model Macroeconomic variables Creditworthy borrowers Car loans data em algorithm

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Doubly truncated expectation and variance of univariate generalized skew-elliptical distributions with applications

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2023年

作者： Zuo, Baishuai Yin, Chuancun Qufu Normal Univ Sch Stat & Data Sci Qufu Shandong Peoples R China

In this article, doubly truncated expectation (DTE) and variance (DTV) of univariate generalized skew-elliptical (GSE) distributions are investigated. In addition, we present an alternative form of DTE and DTV for this class of distributions in terms of the hazard function. This class of distributions includes many skewing distributions, for instance, generalized skew-normal, skew-Student-t, skew-logistic, skew-Laplace, and skew-Pearson type VII distributions. Also, we define truncated generalized skew-elliptical distributions and give the relations between moments of truncated distributions and truncated moments of distributions. Specially, we use the em algorithm to give maximum likelihood estimation of parameters for generalized skew-elliptical distributions. Further, we apply our results to present tail conditional expectation (TCE) and tail variance (TV) for GSE distributions. We also structure an optimal portfolio selection involving DTE and DTV, and give its optimal solution. As an illustrative example, DTE and DTV of a skew-normal random variable are estimated by the Monte Carlo method. Finally, we use real data to fit and select the best distributions, and analysis TCE and TV for the logarithm of adjusted price of three companies (stocks) from S & P (Standard & Poor's) sectors.

关键词： Doubly truncated expectation Doubly truncated variance em algorithm Generalized skew-elliptical distribution Monte Carlo method Tail conditional expectation Tail variance

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Improving model choice in classification: an approach based on clustering of covariance matrices

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STATISTICS AND COMPUTING 2024年第3期34卷 100-100页

作者： Rodriguez-Vitores, David Matran, Carlos Univ Valladolid Dept Stat & Operat Res Paseo Belen 7 Valladolid 47011 Spain Univ Valladolid IMUVA Paseo Belen 7 Valladolid 47011 Spain

This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of clusters of the involved covariance matrices according to a criterion, such as sharing Principal Directions. This and other similarity criteria that arise from the spectral decomposition of a matrix are the bases of the Parsimonious Model. We show that such groupings of covariance matrices can be achieved through simple modifications of the Cem (Classification Expectation Maximization) algorithm. Our approach leads to propose Gaussian Mixture Models for model-based clustering and discriminant analysis, in which covariance matrices are clustered according to a parsimonious criterion, creating intermediate steps between the fourteen widely known parsimonious models. The added versatility not only allows us to obtain models with fewer parameters for fitting the data, but also provides greater interpretability. We show its usefulness for model-based clustering and discriminant analysis, providing algorithms to find approximate solutions verifying suitable size, shape and orientation constraints, and applying them to both simulation and real data examples.

关键词： Parsimonious model Gaussian mixture model Bayesian information criterion Model-based classification em algorithm

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The discrete q-Gaussian distribution Nq(μ, σ²): Properties and parameters estimation

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PHYSICS LETTERS A 2024年 493卷

作者： Ben Mrad, Oumaima Masmoudi, Afif Slaoui, Yousri Univ Sfax Lab Probabil & Stat Sfax Tunisia Univ Poitiers Lab Math & Applicat Poitiers France

We introduce a new discrete distribution, called the centered reduced discrete q-Gaussian N-q(0,1). This distribution connects classical Gaussian, discrete Uniform, and quantum q-Gaussian distributions. In this paper, we extend N-q(0,1) to N-q(mu,sigma(2)), overcoming a limitation of some q-distributions like Diaz and Pariguan's q-Gaussian. Notably, N-q(0,1) has distinct shapes and parameters from the classical counterpart, providing additional flexible modeling approach. Results show the suggested discrete q-Gaussian as a useful alternative to the classical Gaussian for modeling data with hollow values or heavy-tailed tails. We explore properties of N-q(mu,sigma(2)) and apply moments and maximum likelihood methods to estimate its parameters. Our analysis yields a key result on the concavity of the likelihood function, enabling efficient optimization algorithms for parameters estimation. Furthermore, we investigate a finite mixture of discrete q-Gaussians and apply the em algorithm for parameters estimation. Finally, we conduct a simulation study to evaluate the model and estimation methods.

关键词： q-calculus q-distribution q-Gaussian Finite mixture Parametric estimation em algorithm

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Semiparametric regression analysis of partly interval-censored failure time data with application to an AIDS clinical trial

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STATISTICS IN MEDICINE 2021年第20期40卷 4376-4394页

作者： Zhou, Qingning Sun, Yanqing Gilbert, Peter B. Univ N Carolina Dept Math & Stat Charlotte NC 28223 USA Univ Washington Dept Biostat Seattle WA 98195 USA Fred Hutchinson Canc Res Ctr Vaccine & Infect Dis & Publ Hlth Sci Div 1124 Columbia St Seattle WA 98104 USA

Failure time data subject to various types of censoring commonly arise in epidemiological and biomedical studies. Motivated by an AIDS clinical trial, we consider regression analysis of failure time data that include exact and left-, interval-, and/or right-censored observations, which are often referred to as partly interval-censored failure time data. We study the effects of potentially time-dependent covariates on partly interval-censored failure time via a class of semiparametric transformation models that includes the widely used proportional hazards model and the proportional odds model as special cases. We propose an em algorithm for the nonparametric maximum likelihood estimation and show that it unifies some existing approaches developed for traditional right-censored data or purely interval-censored data. In particular, the proposed method reduces to the partial likelihood approach in the case of right-censored data under the proportional hazards model. We establish that the resulting estimator is consistent and asymptotically normal. In addition, we investigate the proposed method via simulation studies and apply it to the motivating AIDS clinical trial.

关键词： AIDS clinical trial em algorithm partly interval‐ censored data semiparametric transformation models survival analysis

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Multiple scaled contaminated normal distribution and its application in clustering

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STATISTICAL MODELLING 2021年第4期21卷 332-358页

作者： Punzo, Antonio Tortora, Cristina Univ Catania Dept Econ & Business Catania Italy San Jose State Univ Dept Math & Stat One Washington Sq San Jose CA 95192 USA

The multivariate contaminated normal (MCN) distribution represents a simple heavy-tailed generalization of the multivariate normal (MN) distribution to model elliptical contoured scatters in the presence of mild outliers (also referred to as 'bad' points herein) and automatically detect bad points. The price of these advantages is two additional parameters: proportion of good observations and degree of contamination. However, in a multivariate setting, only one proportion of good observations and only one degree of contamination may be limiting. To overcome this limitation, we propose a multiple scaled contaminated normal (MSCN) distribution. Among its parameters, we have an orthogonal matrix Gamma. In the space spanned by the vectors (principal components) of Gamma, there is a proportion of good observations and a degree of contamination for each component. Moreover, each observation has a posterior probability of being good with respect to each principal component. Thanks to this probability, the method provides directional robust estimates of the parameters of the nested MN and automatic directional detection of bad points. The term 'directional' is added to specify that the method works separately for each principal component. Mixtures of MSCN distributions are also proposed, and an expectation-maximization algorithm is used for parameter estimation. Real and simulated data are considered to show the usefulness of our mixture with respect to well-established mixtures of symmetric distributions with heavy tails.

关键词： contaminated normal distribution heavy-tailed distributions multiple scaled distributions em algorithm mixture models model-based clustering

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