Non-Fiction Books:

Likelihood-Based Methods for Constrained Parameter Problems

By

Format

Paperback

Customer rating

Click to share your rating 0 ratings (0.0/5.0 average) Thanks for your vote!

Share this product

Likelihood-Based Methods for Constrained Parameter Problems by Da Ju
Unavailable
Sorry, this product is not currently available to order

Description

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)
Release date NZ
January 26th, 2017
Author
Contributor
Created by
Country of Publication
United States
Illustrations
colour illustrations
Imprint
Open Dissertation Press
Dimensions
216x279x8
ISBN-13
9781361043455
Product ID
26646098

Customer reviews

Nobody has reviewed this product yet. You could be the first!

Write a Review

Marketplace listings

There are no Marketplace listings available for this product currently.
Already own it? Create a free listing and pay just 9% commission when it sells!

Sell Yours Here

Help & options

  • If you think we've made a mistake or omitted details, please send us your feedback. Send Feedback
  • If you have a question or problem with this product, visit our Help section. Get Help
Filed under...

Buy this and earn 691 Banana Points