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Gram-Schmidt-fisher scoring algorithm for parameter orthogonalization in MLE

COGENT MATHEMATICS 2016年第1期3卷 Article: 1159847页

作者： Kwagyan, John Apprey, Victor Bonney, George E. Howard Univ Coll Med Design Biostat & Populat Studies Washington DC 20059 USA Howard Univ Coll Med Dept Family Med Washington DC 20059 USA

The estimation of parameters is a key component in statistical modelling and inference. However, parametrization of certain likelihood functions could lead to highly correlated estimates, causing numerical problems, mathematical complexities and difficulty in estimation or erroneous interpretation and subsequently inference. In statistical estimation, the concept of orthogonalization is familiar as a simplifying technique that allows parameters to be estimated independently and thus separates information from each other. We introduce a fisher scoring iterative process that incorporates the Gram-Schmidt orthogonalization technique for maximum likelihood estimation. A finite mixture model for correlated binary data is used to illustrate the implementation of the method with discussion of application to oesophageal cancer data.

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Likelihood-based methods for the zero-one-two inflated Poisson model with applications to biomedicine

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2023年第6期93卷 956-982页

作者： Sun, Yuan Zhao, Shishun Tian, Guo-Liang Tang, Man-Lai Li, Tao Harbin Inst Technol Dept Math Harbin 150001 Heilongjiang Peoples R China Jilin Univ Sch Math Changchun Jilin Peoples R China Southern Univ Sci & Technol Dept Stat & Data Sci Shenzhen Guangdong Peoples R China Brunel Univ London Dept Math Coll Engn Design & Phys Sci Uxbridge Middx England

To model count data with excess zeros, ones and twos, for the first time we introduce a so-called zero-one-two-inflated Poisson (ZOTIP) distribution, including the zero-inflated Poisson (ZIP) and the zero-and-one-inflated Poisson (ZOIP) distributions as two special cases. We establish three equivalent stochastic representations for the ZOTIP random variable to develop important distributional properties of the ZOTIP distribution. The fisher scoring and expectation-maximization (EM) algorithms are derived to obtain the maximum likelihood estimates of parameters of interest. Bootstrap confidence intervals are also provided. Testing hypotheses are considered, simulation studies are conducted, and two real data sets are used to illustrate the proposed methods.

关键词： Bootstrap confidence intervals EM algorithm fisher scoring algorithm zero-and-one-inflated Poisson model zero-one-two-inflated Poisson distribution

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Supervised component generalized linear regression using a PLS-extension of the fisher scoring algorithm

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JOURNAL OF MULTIVARIATE ANALYSIS 2013年 119卷 47-60页

作者： Bry, X. Trottier, C. Verron, T. Mortier, F. Univ Montpellier 2 Inst Math & Modelisat Montpellier F-34095 Montpellier France Univ Montpellier 2 F-34095 Montpellier France ALTADIS Ctr Rech SCR F-45404 Fleury Les Aubrais France Cirad UR B&SEF Biens & Serv Ecosyst Forestiers Tropicaux F-34398 Montpellier France

In the current estimation of a GLM model, the correlation structure of regressors is not used as the basis on which to lean strong predictive dimensions. Looking for linear combinations of regressors that merely maximize the likelihood of the GLM has two major consequences: (1) collinearity of regressors is a factor of estimation instability, and (2) as predictive dimensions may lean on noise, both predictive and explanatory powers of the model are jeopardized. For a single dependent variable, attempts have been made to adapt PLS regression, which solves this problem in the classical Linear Model, to GLM estimation. In this paper, we first discuss the methods thus developed, and then propose a technique, Supervised Component Generalized Linear Regression (SCGLR), that combines PLS regression with GLM estimation in the multivariate context. SCGLR is tested on both simulated and real data. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Supervised component generalized linear regression Generalized linear models PLS regression fisher scoring algorithm

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Multiple arbitrarily inflated Poisson regression analysis

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年

作者： Abusaif, Ihab Kayaci, Burak Kus, Coskun Selcuk Univ Fac Sci Dept Stat Konya Turkiye

In this paper, a new flexible count regression analysis is proposed. For this purpose, a new modification of the Poisson distribution is introduced which generalizes the Poisson, zero-inflated Poisson, zero-one inflated Poisson, and zero-one-two inflated Poisson distributions. Some distributional properties are discussed for the proposed distribution. The fisher scoring and EM algorithms are derived to attain the maximum likelihood estimates of the unknown parameters. An expected fisher information matrix is provided to construct an approximate confidence interval for the parameters. Using the modified Poisson distribution, an arbitrary multiply inflated counting regression model is proposed. The performance of the maximum likelihood methodology is investigated with a simulation study for the distribution and count regression model. Finally, two practical data sets are analyzed and the superiority of the proposed model is demonstrated among others.

关键词： Count data EM algorithm fisher scoring algorithm Inflated count regression model Zero-inflated Poisson distribution

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A new hybrid discriminative/generative model using the full-covariance multivariate generalized Gaussian mixture models

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SOFT COMPUTING 2020年第14期24卷 10611-10628页

作者： Najar, Fatma Bourouis, Sami Bouguila, Nizar Belghith, Safya Univ Tunis El Manar ENIT Lab RISC Robot Informat & Syst Complexes Tunis 1002 Tunisia Univ Tunis El Manar ENIT LR SITI Lab Signal Image & Technol Informat Tunis Tunisia Taif Univ Coll Comp & Informat Technol At Taif Saudi Arabia Concordia Univ CIISE Montreal PQ H3G 1T7 Canada

Discriminative models have been shown to be more advantageous for pattern recognition problem in machine learning. For this study, the main focus is developing a new hybrid model that combines the advantages of a discriminative technique namely the support vector machines (SVM) with the full efficiency offered through covariance multivariate generalized Gaussian mixture models (MGGMM). This new hybrid MGGMM applies the fisher and Kullback-Leibler kernels derived from MGGMM to improve the kernel function of SVM. This approach is based on two different learning techniques explicitly: the fisher scoring algorithm and the Bayes inference technique based on Markov Chain Monte Carlo and Metropolis-Hastings algorithm. These learning methods work with two model selection approaches (minimum message length and marginal likelihood) to determine the number of clusters. The effectiveness of the framework is demonstrated through extensive experiments including synthetic datasets, facial expression recognition and human activity recognition.

关键词： Multivariate generalized Gaussian mixture Support vector machines kernels fisher scoring algorithm Bayesian learning Facial expression recognition Human activity recognition

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Cointegration models with non Gaussian GARCH innovations

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METRON-INTERNATIONAL JOURNAL OF STATISTICS 2018年第1期76卷 83-98页

作者： John, Nimitha Narayana, Balakrishna Cochin Univ Sci & Technol Dept Statis Cochin 682022 Kerala India

This paper presents the estimation procedures for a bivariate cointegration model when the errors are generated by a constant conditional correlation model. In particular, the method of maximum likelihood is discussed when the errors follow Generalised Autoregressive Conditional Hetroskedastic (GARCH) models with Gaussian and some non Gaussian innovations. The method of estimation is illustrated using simulated observations. Data analysis is provided to highlight the applications of the proposed models.

关键词： Cointegration fisher scoring algorithm Generalised autoregressive conditional heterosedasticity Volatility Models

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Inflated assessments of disability

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JOURNAL OF APPLIED STATISTICS 2017年第10期44卷 1743-1760页

作者： Longford, Nicholas T. Imperial Coll Dept Med London England

A medical examination provides a key input into decisions about disability pension and other forms of income support or compensation that are justified on medical grounds. The result of examining an individual is often communicated by means of a score, and inflation of such scores is a well-known problem. We estimate the extent of inflation of scores from a set of disability assessments using a model based on the discrete linear distribution. We explore some extensions within the framework of a sensitivity analysis.

关键词： Assessment disability score discrete linear distribution fisher scoring algorithm score inflation 62F10 62F30

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Logistic regression with misclassification in binary outcome variables: a method and software

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Behaviormetrika 2017年第2期44卷 447-476页

作者： Liu, Haiyan Zhang, Zhiyong Department of Psychology University of Notre Dame 118 Haggar Hall Notre Dame 46556 IN United States

Measurement error in continuous, normally distributed data is well known in the literature. Measurement error in a binary outcome variable, however, remains under-studied. Misclassification is the error in categorical data in which the observed category is different from the underlying one. In this study, we show, through a Monte Carlo simulation study, that there are non-ignorable biases in parameter estimates if the misclassification is ignored. To deal with the influence of the misclassification, we introduce a model with false-positive and false-negative misclassification parameters. Such a model can not only estimate the underlying association between the dependent and independent variables, but it also provides information on the extent of the misclassification. To estimate the model, a maximum likelihood estimation method based on a fisher scoring algorithm is utilized. A simulation study is conducted to evaluate the performance, and a real data example is given to demonstrate the usefulness of the new model. An R package is developed to aid the application of the model. © 2017, The Behaviormetric Society.

关键词： Binary outcome fisher scoring algorithm Logistic regression Marijuana use Misclassification

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Local-linear likelihood estimation of geographically weighted generalised linear models

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JOURNAL OF SPATIAL SCIENCE 2016年第1期61卷 99-117页

作者： Xu, Min Mei, Chang-Lin Hou, Shu-Jing Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China Tibet Univ Nationalities Sch Finance & Econ Xianyang Peoples R China

Geographically weighted generalised linear models are an extension of the geographically weighted regression models in order to handle such types of the response variables that their distributions follow a member of the exponential family of distributions. In view of the advantages of the local-linear fitting technique, we propose in this paper a local-linear likelihood estimation approach for geographically weighted generalised linear models to improve the accuracy of the coefficient estimators. A fisher scoring algorithm is formulated to compute the estimators of the coefficients. Simulations are conducted for some typical geographically weighted generalised linear models to evaluate the performance of the proposed estimation method and the results show that, compared to the existing local-constant likelihood estimation, the local-linear likelihood method can evidently improve the accuracy of the coefficient estimators. A real-world data-set is finally analysed to demonstrate the application of the proposed approach.

关键词： fisher scoring algorithm local-linear likelihood estimation exponential family of distributions geographically weighted generalised linear model spatial non-stationarity

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Information Splitting for Big Data Analytics 8

Information Splitting for Big Data Analytics

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8th International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC)

作者： Zhu, Shengxin Gu, Tongxiang Xu, Xiaowen Mo, Zeyao Inst Appl Phys & Computat Math Lab Computat Phys POB 8009 Beijing 100088 Peoples R China

ISBN: (纸本)9781509051540

Many statistical models require an estimation of unknown (co)-variance parameter(s). The estimation is usually obtained by maximizing a log-likelihood which involves log determinant terms. In principle, one requires the observed information-the negative Hessian matrix or the second derivative of the log-likelihood-to obtain an accurate maximum likelihood estimator according to the Newton method. When one uses the fisher information, the expect value of the observed information, a simpler algorithm than the Newton method is obtained as the fisher scoring algorithm. With the advance in high-throughput technologies in the biological sciences, recommendation systems and social networks, the sizes of data sets-and the corresponding statistical models-have suddenly increased by several orders of magnitude. Neither the observed information nor the fisher information is easy to obtained for these big data sets. This paper introduces an information splitting technique to simplify the computation. After splitting the mean of the observed information and the fisher information, an simpler approximate Hessian matrix for the log-likelihood can be obtained. This approximated Hessian matrix can significantly reduce computations, and makes the linear mixed model applicable for big data sets. Such a spitting and simpler formulas heavily depend on matrix algebra transforms, and applicable to large scale breeding model, genetics wide association analysis.

关键词： Observed information matrix fisher information matrix fisher scoring algorithm linear mixed model breeding model geno-wide-association variance parameter estimation

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