APPLICATIONS OF EMPIRICAL LIKELIHOOD TO ZERO-INFLATED DATA AND EPIDEMIC CHANGE POINT

APPLICATIONS OF EMPIRICAL LIKELIHOOD TO ZERO-INFLATED DATA AND EPIDEMIC CHANGE POINT
Author: Junvie Montealto Pailden
Publisher:
Total Pages: 89
Release: 2013
Genre: Analysis of means
ISBN:
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Many studies in health care deal with zero-inflated data sets characterized by a significant proportion of zero and highly skewed positive values. Although it is a common practice to use the median instead of the mean as the measure of central location in skewed data, many applications require the use of the mean. For instance, the mean can be used to recover the total medical cost which reflects the entire expenditure on health care in a given patient population. For testing the value of a mean, the empirical likelihood method offers the benefit of making no distributional assumptions beyond some mild moment conditions while retaining the same advantages that parametric likelihood based tests enjoyed. In this dissertation, we proposed an empirical likelihood ratio test for the difference between means of two zero-inflated samples. The proposed test was derived by jointly specifying the empirical likelihood for the mean parameter and the probability of taking zero value in the data. There are two unique features in this procedure. One is that the information contained in the zero observations is fully utilized and that the proposed test is insensitive to the skewness of the non-zero observations. We derive an asymptotic distribution that will be used to calibrate the statistic in testing the null hypothesis of no mean difference. We also extend the procedure to testing the mean equality of several independent zero-inflated populations. As a benchmark for comparison against conventional tests, we investigate the empirical type 1 error and power rates in finite sample settings. Both the proposed two sample test for the mean difference and the equality of means between three or more populations exhibits comparable if not superior finite sample performance. Another application of empirical likelihood approach that we consider is on detecting epidemic change point in a sequence of observations. Under some mild conditions, the asymptotic null distribution of the test statistic is showed to be an extreme distribution. Simulations indicate that the proposed test performs at par if not better than other available tests while enjoying less constraint on the data distribution.

Count Time Series

Count Time Series
Author: Konstantinos Fokianos
Publisher: CRC Press
Total Pages: 220
Release: 2020-06-30
Genre:
ISBN: 9781482248050
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Robust Regression and Outlier Detection

Robust Regression and Outlier Detection
Author: Peter J. Rousseeuw
Publisher: John Wiley & Sons
Total Pages: 329
Release: 2005-02-25
Genre: Mathematics
ISBN: 0471725374
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WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selectedbooks that have been made more accessible to consumers in an effortto increase global appeal and general circulation. With these newunabridged softcover volumes, Wiley hopes to extend the lives ofthese works by making them available to future generations ofstatisticians, mathematicians, and scientists. "The writing style is clear and informal, and much of thediscussion is oriented to application. In short, the book is akeeper." –Mathematical Geology "I would highly recommend the addition of this book to thelibraries of both students and professionals. It is a usefultextbook for the graduate student, because it emphasizes both thephilosophy and practice of robustness in regression settings, andit provides excellent examples of precise, logical proofs oftheorems. . . .Even for those who are familiar with robustness, thebook will be a good reference because it consolidates the researchin high-breakdown affine equivariant estimators and includes anextensive bibliography in robust regression, outlier diagnostics,and related methods. The aim of this book, the authors tell us, is‘to make robust regression available for everyday statisticalpractice.’ Rousseeuw and Leroy have included all of thenecessary ingredients to make this happen." –Journal of the American Statistical Association

Applying Generalized Linear Models

Applying Generalized Linear Models
Author: James K. Lindsey
Publisher: Springer Science & Business Media
Total Pages: 265
Release: 2008-01-15
Genre: Mathematics
ISBN: 038722730X
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This book describes how generalised linear modelling procedures can be used in many different fields, without becoming entangled in problems of statistical inference. The author shows the unity of many of the commonly used models and provides readers with a taste of many different areas, such as survival models, time series, and spatial analysis, and of their unity. As such, this book will appeal to applied statisticians and to scientists having a basic grounding in modern statistics. With many exercises at the end of each chapter, it will equally constitute an excellent text for teaching applied statistics students and non- statistics majors. The reader is assumed to have knowledge of basic statistical principles, whether from a Bayesian, frequentist, or direct likelihood point of view, being familiar at least with the analysis of the simpler normal linear models, regression and ANOVA.

Ecological Models and Data in R

Ecological Models and Data in R
Author: Benjamin M. Bolker
Publisher: Princeton University Press
Total Pages: 408
Release: 2008-07-21
Genre: Computers
ISBN: 0691125228
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Introduction and background; Exploratory data analysis and graphics; Deterministic functions for ecological modeling; Probability and stochastic distributions for ecological modeling; Stochatsic simulation and power analysis; Likelihood and all that; Optimization and all that; Likelihood examples; Standar statistics revisited; Modeling variance; Dynamic models.

Generalized Additive Models

Generalized Additive Models
Author: Simon Wood
Publisher: CRC Press
Total Pages: 412
Release: 2006-02-27
Genre: Mathematics
ISBN: 1584884746
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Now in widespread use, generalized additive models (GAMs) have evolved into a standard statistical methodology of considerable flexibility. While Hastie and Tibshirani's outstanding 1990 research monograph on GAMs is largely responsible for this, there has been a long-standing need for an accessible introductory treatment of the subject that also emphasizes recent penalized regression spline approaches to GAMs and the mixed model extensions of these models. Generalized Additive Models: An Introduction with R imparts a thorough understanding of the theory and practical applications of GAMs and related advanced models, enabling informed use of these very flexible tools. The author bases his approach on a framework of penalized regression splines, and builds a well-grounded foundation through motivating chapters on linear and generalized linear models. While firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of the freely available R software helps explain the theory and illustrates the practicalities of linear, generalized linear, and generalized additive models, as well as their mixed effect extensions. The treatment is rich with practical examples, and it includes an entire chapter on the analysis of real data sets using R and the author's add-on package mgcv. Each chapter includes exercises, for which complete solutions are provided in an appendix. Concise, comprehensive, and essentially self-contained, Generalized Additive Models: An Introduction with R prepares readers with the practical skills and the theoretical background needed to use and understand GAMs and to move on to other GAM-related methods and models, such as SS-ANOVA, P-splines, backfitting and Bayesian approaches to smoothing and additive modelling.

Statistical Models in S

Statistical Models in S
Author: T.J. Hastie
Publisher: Routledge
Total Pages: 542
Release: 2017-11-01
Genre: Mathematics
ISBN: 1351414224
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Statistical Models in S extends the S language to fit and analyze a variety of statistical models, including analysis of variance, generalized linear models, additive models, local regression, and tree-based models. The contributions of the ten authors-most of whom work in the statistics research department at AT&T Bell Laboratories-represent results of research in both the computational and statistical aspects of modeling data.

Frailty Models in Survival Analysis

Frailty Models in Survival Analysis
Author: Andreas Wienke
Publisher: CRC Press
Total Pages: 324
Release: 2010-07-26
Genre: Mathematics
ISBN: 9781420073911
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The concept of frailty offers a convenient way to introduce unobserved heterogeneity and associations into models for survival data. In its simplest form, frailty is an unobserved random proportionality factor that modifies the hazard function of an individual or a group of related individuals. Frailty Models in Survival Analysis presents a comprehensive overview of the fundamental approaches in the area of frailty models. The book extensively explores how univariate frailty models can represent unobserved heterogeneity. It also emphasizes correlated frailty models as extensions of univariate and shared frailty models. The author analyzes similarities and differences between frailty and copula models; discusses problems related to frailty models, such as tests for homogeneity; and describes parametric and semiparametric models using both frequentist and Bayesian approaches. He also shows how to apply the models to real data using the statistical packages of R, SAS, and Stata. The appendix provides the technical mathematical results used throughout. Written in nontechnical terms accessible to nonspecialists, this book explains the basic ideas in frailty modeling and statistical techniques, with a focus on real-world data application and interpretation of the results. By applying several models to the same data, it allows for the comparison of their advantages and limitations under varying model assumptions. The book also employs simulations to analyze the finite sample size performance of the models.

Mathematical Statistics with Applications in R

Mathematical Statistics with Applications in R
Author: Kandethody M. Ramachandran
Publisher: Elsevier
Total Pages: 825
Release: 2014-09-14
Genre: Mathematics
ISBN: 012417132X
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Mathematical Statistics with Applications in R, Second Edition, offers a modern calculus-based theoretical introduction to mathematical statistics and applications. The book covers many modern statistical computational and simulation concepts that are not covered in other texts, such as the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. By combining the discussion on the theory of statistics with a wealth of real-world applications, the book helps students to approach statistical problem solving in a logical manner.This book provides a step-by-step procedure to solve real problems, making the topic more accessible. It includes goodness of fit methods to identify the probability distribution that characterizes the probabilistic behavior or a given set of data. Exercises as well as practical, real-world chapter projects are included, and each chapter has an optional section on using Minitab, SPSS and SAS commands. The text also boasts a wide array of coverage of ANOVA, nonparametric, MCMC, Bayesian and empirical methods; solutions to selected problems; data sets; and an image bank for students.Advanced undergraduate and graduate students taking a one or two semester mathematical statistics course will find this book extremely useful in their studies. Step-by-step procedure to solve real problems, making the topic more accessible Exercises blend theory and modern applications Practical, real-world chapter projects Provides an optional section in each chapter on using Minitab, SPSS and SAS commands Wide array of coverage of ANOVA, Nonparametric, MCMC, Bayesian and empirical methods

Seamless R and C++ Integration with Rcpp

Seamless R and C++ Integration with Rcpp
Author: Dirk Eddelbuettel
Publisher: Springer Science & Business Media
Total Pages: 236
Release: 2013-06-04
Genre: Computers
ISBN: 146146868X
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Rcpp is the glue that binds the power and versatility of R with the speed and efficiency of C++. With Rcpp, the transfer of data between R and C++ is nearly seamless, and high-performance statistical computing is finally accessible to most R users. Rcpp should be part of every statistician's toolbox. -- Michael Braun, MIT Sloan School of Management "Seamless R and C++ integration with Rcpp" is simply a wonderful book. For anyone who uses C/C++ and R, it is an indispensable resource. The writing is outstanding. A huge bonus is the section on applications. This section covers the matrix packages Armadillo and Eigen and the GNU Scientific Library as well as RInside which enables you to use R inside C++. These applications are what most of us need to know to really do scientific programming with R and C++. I love this book. -- Robert McCulloch, University of Chicago Booth School of Business Rcpp is now considered an essential package for anybody doing serious computational research using R. Dirk's book is an excellent companion and takes the reader from a gentle introduction to more advanced applications via numerous examples and efficiency enhancing gems. The book is packed with all you might have ever wanted to know about Rcpp, its cousins (RcppArmadillo, RcppEigen .etc.), modules, package development and sugar. Overall, this book is a must-have on your shelf. -- Sanjog Misra, UCLA Anderson School of Management The Rcpp package represents a major leap forward for scientific computations with R. With very few lines of C++ code, one has R's data structures readily at hand for further computations in C++. Hence, high-level numerical programming can be made in C++ almost as easily as in R, but often with a substantial speed gain. Dirk is a crucial person in these developments, and his book takes the reader from the first fragile steps on to using the full Rcpp machinery. A very recommended book! -- Søren Højsgaard, Department of Mathematical Sciences, Aalborg University, Denmark "Seamless R and C ++ Integration with Rcpp" provides the first comprehensive introduction to Rcpp. Rcpp has become the most widely-used language extension for R, and is deployed by over one-hundred different CRAN and BioConductor packages. Rcpp permits users to pass scalars, vectors, matrices, list or entire R objects back and forth between R and C++ with ease. This brings the depth of the R analysis framework together with the power, speed, and efficiency of C++. Dirk Eddelbuettel has been a contributor to CRAN for over a decade and maintains around twenty packages. He is the Debian/Ubuntu maintainer for R and other quantitative software, edits the CRAN Task Views for Finance and High-Performance Computing, is a co-founder of the annual R/Finance conference, and an editor of the Journal of Statistical Software. He holds a Ph.D. in Mathematical Economics from EHESS (Paris), and works in Chicago as a Senior Quantitative Analyst.