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Computation Of Maximum Likelihood Estimates For The Lognormal Probability Model Using Constrained Nonlinear Optimization
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Book Synopsis Computation of Maximum Likelihood Estimates for the Lognormal Probability Model Using Constrained Nonlinear Optimization by : Wade Harrison Shaw
Download or read book Computation of Maximum Likelihood Estimates for the Lognormal Probability Model Using Constrained Nonlinear Optimization written by Wade Harrison Shaw and published by . This book was released on 1978 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Application of Nonlinear Programming to Constrained Maximum Likelihood Estimation by : Lester M. Rydl
Download or read book The Application of Nonlinear Programming to Constrained Maximum Likelihood Estimation written by Lester M. Rydl and published by . This book was released on 1978 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Likelihood-Based Methods for Constrained Parameter Problems by : Da Ju
Download or read book Likelihood-Based Methods for Constrained Parameter Problems written by Da Ju and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Likelihood-based Methods for Constrained Parameter Problems" by Da, Ju, 鞠达, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Truncated observations for some applications and parameters with a certain kind of constraints may provide a kind of prior information for the data analysis. Such information, if integrated into the scientific study, can significantly improve the result of statistical inferences. In order to sufficiently utilize such information, these truncations or constraints are taken into consideration in the modeling process. This thesis, therefore, aims to analyze truncated normal data and to study the constrained parameter problems. In practice, the normal distribution is widely used to model continuous data. However, when the data fall in a certain interval, truncated normal distribution becomes a better choice. Through stochastically representing the normal random variable as a mixture of a truncated normal random variable and its complementary random variable, Chapter 2 proposes two new expectation-maximization (EM) algorithms to calculate maximum likelihood estimates of parameters in truncated normal distribution. Furthermore, in the analyses of two real datasets based on Akaike information criterion (AIC) and Bayesian information criterion (BIC), it is found that the truncated normal distribution performs better than the half normal, the folded normal and the folded normal slash distributions. Although Type I multivariate zero-inflated Poisson (ZIP) distribution has been recently proposed to model zero inflated correlated multivariate discrete data by Liu and Tian (2015), the statistical methods for this multivariate distribution with constrained parameters are still lacking. Chapter 3 proposes an SR-based EM algorithm (Dempster et al., 1977) and a Q-based EM algorithm aided by the De Pierro algorithm (De Pierro, 1995) for the constrained multivariate ZIP models after studying two constrained types. Generalized linear model (GLM) with canonical link function is a flexible and useful generalization of the ordinary linear regression. However, no thorough studies on the constrained estimation problem in GLM have been done so far. According to the Karush-Kuhn-Tucker conditions, Chapter 4 derives two asymptotic properties of the constrained estimators. Meanwhile, via transferring the constrained optimization problem of maximizing a log-likelihood function to the problem of maximizing a separable surrogate function with a diagonal Hessian matrix subject to box constraints, the constrained optimization problem is now equivalent to separately maximizing several one dimensional concave functions with a lower bound and an upper bound and has therefore an explicit solution. Furthermore, after this transformation, a modified De Pierro (DP) algorithm is developed to calculate the maximum likelihood estimates (MLE) of the regression coefficients subject to linear or box inequality restrictions. Lastly, the analyses of real datasets and simulations are conducted to evaluate the proposed methods in this thesis. Subjects: Missing observations (Statistics)
Book Synopsis Maximum Likelihood Estimation by : Scott R. Eliason
Download or read book Maximum Likelihood Estimation written by Scott R. Eliason and published by SAGE Publications, Incorporated. This book was released on 1993-08-09 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a short introduction to Maximum Likelihood (ML) Estimation. It provides a general modeling framework that utilizes the tools of ML methods to outline a flexible modeling strategy that accommodates cases from the simplest linear models (such as the normal error regression model) to the most complex nonlinear models linking endogenous and exogenous variables with non-normal distributions. Using examples to illustrate the techniques of finding ML estimators and estimates, the author discusses what properties are desirable in an estimator, basic techniques for finding maximum likelihood solutions, the general form of the covariance matrix for ML estimates, the sampling distribution of ML estimators; the use of ML in the normal as well as other distributions, and some useful illustrations of likelihoods.
Book Synopsis The Application of Nonlinear Programming to Constrained Maximum Likelihood Estimation by : Lester Melvin Rydl
Download or read book The Application of Nonlinear Programming to Constrained Maximum Likelihood Estimation written by Lester Melvin Rydl and published by . This book was released on 1978 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Maximum Likelihood Estimation of Parameters with Constraints in Normal and Multinomial Distributions by : HUITIAN. XUE
Download or read book Maximum Likelihood Estimation of Parameters with Constraints in Normal and Multinomial Distributions written by HUITIAN. XUE and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Maximum Likelihood Estimation of Parameters With Constraints in Normal and Multinomial Distributions" by Huitian, Xue, 薛惠天, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Motivated by problems in medicine, biology, engineering and economics, con- strained parameter problems arise in a wide variety of applications. Among them the application to the dose-response of a certain drug in development has attracted much interest. To investigate such a relationship, we often need to conduct a dose- response experiment with multiple groups associated with multiple dose levels of the drug. The dose-response relationship can be modeled by a shape-restricted normal regression. We develop an iterative two-step ascent algorithm to estimate normal means and variances subject to simultaneous constraints. Each iteration consists of two parts: an expectation{maximization (EM) algorithm that is utilized in Step 1 to compute the maximum likelihood estimates (MLEs) of the restricted means when variances are given, and a newly developed restricted De Pierro algorithm that is used in Step 2 to find the MLEs of the restricted variances when means are given. These constraints include the simple order, tree order, umbrella order, and so on. A bootstrap approach is provided to calculate standard errors of the restricted MLEs. Applications to the analysis of two real datasets on radioim-munological assay of cortisol and bioassay of peptides are presented to illustrate the proposed methods. Liu (2000) discussed the maximum likelihood estimation and Bayesian estimation in a multinomial model with simplex constraints by formulating this constrained parameter problem into an unconstrained parameter problem in the framework of missing data. To utilize the EM and data augmentation (DA) algorithms, he introduced latent variables {Zil;Yil} (to be defined later). However, the proposed DA algorithm in his paper did not provide the necessary individual conditional distributions of Yil given (the observed data and) the updated parameter estimates. Indeed, the EM algorithm developed in his paper is based on the assumption that{ Yil} are fixed given values. Fortunately, the EM algorithm is invariant under any choice of the value of Yil, so the final result is always correct. We have derived the aforesaid conditional distributions and hence provide a valid DA algorithm. A real data set is used for illustration. DOI: 10.5353/th_b4785001 Subjects: Estimation theory Parameter estimation
Book Synopsis Nonlinear Statistical Estimation with Numerical Maximum Likelihood by : Gerald Gerard Brown
Download or read book Nonlinear Statistical Estimation with Numerical Maximum Likelihood written by Gerald Gerard Brown and published by . This book was released on 1974 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics of maximum likelihood estimation and nonlinear programming are developed thoroughly with emphasis on the numerical details of obtaining estimates from highly nonlinear models. Parametric estimation is discussed with the three parameter Weibull family of densities serving as an example. A general nonlinear programming method is discussed for both first and second order representations of the maximum likelihood estimaton, as well as a hybrid of both approaches. A new class of constrained parametric estimators is introduced with numerical methods for their determination. Structural estimation with maximum likelihood is examined, and a Bernoulli regression technique is presented.
Book Synopsis Maximum Penalized Likelihood Estimation by : P.P.B. Eggermont
Download or read book Maximum Penalized Likelihood Estimation written by P.P.B. Eggermont and published by Springer Nature. This book was released on 2020-12-15 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with parametric and nonparametric density estimation from the maximum (penalized) likelihood point of view, including estimation under constraints. The focal points are existence and uniqueness of the estimators, almost sure convergence rates for the L1 error, and data-driven smoothing parameter selection methods, including their practical performance. The reader will gain insight into technical tools from probability theory and applied mathematics.
Book Synopsis Estimating Density Functions by : Michael X. Dong
Download or read book Estimating Density Functions written by Michael X. Dong and published by . This book was released on 1996 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Maximum Likelihood Estimation with Stata, Fourth Edition by : William Gould
Download or read book Maximum Likelihood Estimation with Stata, Fourth Edition written by William Gould and published by Stata Press. This book was released on 2010-10-27 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximum Likelihood Estimation with Stata, Fourth Edition is written for researchers in all disciplines who need to compute maximum likelihood estimators that are not available as prepackaged routines. Readers are presumed to be familiar with Stata, but no special programming skills are assumed except in the last few chapters, which detail how to add a new estimation command to Stata. The book begins with an introduction to the theory of maximum likelihood estimation with particular attention on the practical implications for applied work. Individual chapters then describe in detail each of the four types of likelihood evaluator programs and provide numerous examples, such as logit and probit regression, Weibull regression, random-effects linear regression, and the Cox proportional hazards model. Later chapters and appendixes provide additional details about the ml command, provide checklists to follow when writing evaluators, and show how to write your own estimation commands.
Book Synopsis Maximum Likelihood Estimation Procedures for Categorical Data by : Rene Ehlers
Download or read book Maximum Likelihood Estimation Procedures for Categorical Data written by Rene Ehlers and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Approaches for Maximum Likelihood Estimation for Nonlinearmixed Models by :
Download or read book Computational Approaches for Maximum Likelihood Estimation for Nonlinearmixed Models written by and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The nonlinear mixed model is an important tool for analyzingpharmacokinetic and other repeated-measures data. In particular, these models are used when the measured response for anindividual, has a nonlinear relationship with unknown, random, individual-specificparameters, . Ideally, the method of maximum likelihood is used to find estimates forthe parameters ofthe model after integrating out the random effects in the conditionallikelihood. However, closed form solutions tothe integral are generally not available. As a result, methods have beenpreviously developed to find approximatemaximum likelihood estimates for the parameters in the nonlinear mixedmodel. These approximate methods include FirstOrder linearization, Laplace's approximation, importance sampling, andGaussian quadrature. The methods are availabletoday in several software packages for models of limited sophistication;constant conditional error variance is requiredfor proper utilization of most software. In addition, distributionalassumptions are needed. This work investigates howrobust two of these methods, First Order linearization and Laplace'sapproximation, are to these assumptions. The findingis that Laplace's approximation performs well, resulting in betterestimation than first order linearization when bothmodels converge to a solution. A method must provide good estimates of the likelihood at points inthe parameter space near the solution. This workcompares this ability among the numerical integration techniques, Gaussian quadrature, importance sampling, and Laplace'sapproximation. A new "scaled" and "centered" version of Gaussianquadrature is found to be the most accurate technique. In addition, the technique requires evaluation of the integrand at onlya few abscissas. Laplace's method also performs well; it is more accurate than importance sampling with even 100importance samples over two dimensions. Even so, Laplace's method still does not perform as well as Gaussian quadrature. Overall, Laplace's a.
Book Synopsis Maximum-Likelihood Estimation and Scoring Under Parametric Constraints by :
Download or read book Maximum-Likelihood Estimation and Scoring Under Parametric Constraints written by and published by . This book was released on 2006 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximum likelihood (ML) estimation is a popular approach in solving many signal processing problems. Many of these problems cannot be solved analytically and so numerical techniques such as the method of scoring are applied. However, in many scenarios, it is desirable to modify the ML problem with the inclusion of additional side information. Often this side information is in the form of parametric constraints which the ML estimate (MLE) must now satisfy. We examine the asymptotic normality of the constrained ML (CML) problem and show that it is still consistent as well as asymptotically efficient (with respect to the constrained Cramer-Rao bound). We also generalize the method of scoring to include the constraints, and satisfy the constraints after each iterate. Convergence properties and examples verify the usefulness of the constrained scoring approach. As a particular example, an alternative and more general CML estimator is developed for the linear model with linear constraints.
Book Synopsis Maximum Likelihood Estimation of Misspecified Models by : T. Fomby
Download or read book Maximum Likelihood Estimation of Misspecified Models written by T. Fomby and published by Elsevier. This book was released on 2003-12-12 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comparative study of pure and pretest estimators for a possibly misspecified two-way error component model / Badi H. Baltagi, Georges Bresson, Alain Pirotte -- Estimation, inference, and specification testing for possibly misspecified quantile regression / Tae-Hwan Kim, Halbert White -- Quasimaximum likelihood estimation with bounded symmetric errors / Douglas Miller, James Eales, Paul Preckel -- Consistent quasi-maximum likelihood estimation with limited information / Douglas Miller, Sang-Hak Lee -- An examination of the sign and volatility switching arch models under alternative distributional assumptions / Mohamed F. Omran, Florin Avram -- estimating a linear exponential density when the weighting matrix and mean parameter vector are functionally related / Chor-yiu Sin -- Testing in GMM models without truncation / Timothy J. Vogelsang -- Bayesian analysis of misspecified models with fixed effects / Tiemen Woutersen -- Tests of common deterministic trend slopes applied to quarterly global temperature data / Thomas B. Fomby, Timothy J. Vogelsang -- The sandwich estimate of variance / James W. Hardin -- Test statistics and critical values in selectivity models / R. Carter Hill, Lee C. Adkins, Keith A. Bender -- Introduction / Thomas B Fomby, R. Carter Hill.
Book Synopsis Maximum Likelihood Estimation for Constrained Or Missing Data Models by : Alan E. Gelfand
Download or read book Maximum Likelihood Estimation for Constrained Or Missing Data Models written by Alan E. Gelfand and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1989 with total page 1134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Approaches for Maximum Likelihood Estimation for Nonlinear Mixed Models by : Alan Hughes Hartford
Download or read book Computational Approaches for Maximum Likelihood Estimation for Nonlinear Mixed Models written by Alan Hughes Hartford and published by . This book was released on 2000 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: Nonlinear regression, Mixed models, Maximum likelihood, Laplace's approximation, Stochastic approximation.
