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Maximum likelihood estimation and inference : with examples in R, SAS and ADMB /
"Applied Likelihood Methods provides an accessible and practical introduction to likelihood modeling, supported by examples and software. The book features applications from a range of disciplines, including statistics, medicine, biology, and ecology. The methods are implemented in SAS--the mos...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Chichester, West Sussex, United Kingdom :
John Wiley & Sons, Ltd.,
2011.
|
| Colección: | Statistics in practice.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Millar, R. B. |q (Russell B.), |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjKBhRcJHvYwqcj4dpFBj3 | |
| 245 | 1 | 0 | |a Maximum likelihood estimation and inference : |b with examples in R, SAS and ADMB / |c Russell B. Millar. |
| 264 | 1 | |a Chichester, West Sussex, United Kingdom : |b John Wiley & Sons, Ltd., |c 2011. | |
| 300 | |a 1 online resource (xvi, 357 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Statistics in practice | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Part I. Preliminaries -- Part II. Pragmatics -- Part III. Theoretical foundations. | |
| 520 | |a "Applied Likelihood Methods provides an accessible and practical introduction to likelihood modeling, supported by examples and software. The book features applications from a range of disciplines, including statistics, medicine, biology, and ecology. The methods are implemented in SAS--the most widely used statistical software package--and the data sets and SAS code are provided on a Web site, enabling the reader to use the methods to solve problems in their own work. This book serves as an ideal text for applied scientists and researchers and graduate students of statistics"-- |c Provided by publisher. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Estimation theory. | |
| 650 | 0 | |a Chance |x Mathematical models. | |
| 650 | 4 | |a Mathematics. | |
| 650 | 4 | |a Physical Sciences & Mathematics. | |
| 650 | 4 | |a Mathematical Statistics. | |
| 650 | 6 | |a Théorie de l'estimation. | |
| 650 | 6 | |a Hasard |x Modèles mathématiques. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Estimation theory |2 fast | |
| 758 | |i has work: |a Maximum likelihood estimation and inference (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGVptVC4qm4HvR4xKcMTf3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Millar, R.B. (Russell B.). |t Maximum likelihood estimation and inference. |d Chichester, West Sussex, United Kingdom : John Wiley & Sons, Ltd., 2011 |w (DLC) 2011013225 |
| 830 | 0 | |a Statistics in practice. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=697473 |z Texto completo |
| 880 | 8 | |6 505-00/(S |a 10.6.4 GLMM vs GEE -- 10.7 State-space model for count data -- 10.8 ADMB template files -- 10.8.1 One-way linear random-effects model using REML -- 10.8.2 Nonlinear crossed mixed-effects model -- 10.8.3 Generalized linear mixed model using GREML -- 10.8.4 State-space model for count data -- 10.9 Exercises -- Part III: THEORETICAL FOUNDATIONS -- 11 Cramér-Rao inequality and Fisher information -- 11.1 Introduction -- 11.1.1 Notation -- 11.2 The Cramér-Rao inequality for θ ε R -- 11.3 Cramér-Rao inequality for functions of θ -- 11.4 Alternative formulae for I (θ) -- 11.5 The iid data case -- 11.6 The multi-dimensional case, θ ε Θ c Rs -- 11.6.1 Parameter orthogonality -- 11.6.2 Alternative formulae for I(θ) -- 11.6.3 Fisher information for re-parameterized models -- 11.7 Examples of Fisher information calculation -- 11.7.1 Normal(μ, σ2) -- 11.7.2 Exponential family distributions -- 11.7.3 Linear regression model -- 11.7.4 Nonlinear regression model -- 11.7.5 Generalized linear model with canonical link function -- 11.7.6 Gamma(α, β) -- 11.8 Exercises -- 12 Asymptotic theory and approximate normality -- 12.1 Introduction -- 12.2 Consistency and asymptotic normality -- 12.2.1 Asymptotic normality, θ ε R -- 12.2.2 Asymptotic normality: θ ε Rs -- 12.2.3 Asymptotic normality of g(θ) ε Rp -- 12.2.4 Asymptotic normality under model misspecification -- 12.2.5 Asymptotic normality of M-estimators -- 12.2.6 The non-iid case -- 12.3 Approximate normality -- 12.3.1 Estimation of the approximate variance -- 12.3.2 Approximate normality of M-estimators -- 12.4 Wald tests and confidence regions -- 12.4.1 Wald test statistics -- 12.4.2 Wald confidence intervals and regions -- 12.5 Likelihood ratio test statistic -- 12.5.1 Likelihood ratio test: θ ε R -- 12.5.2 Likelihood ratio test for θ ε Rs, and g(θ) ε Rp -- 12.6 Rao-score test statistic -- 12.7 Exercises. | |
| 880 | 0 | |6 505-00/(S |a Maximum Likelihood Estimation and Inference: With Examples in R, SAS and ADMB -- Contents -- Preface -- Part I: PRELIMINARIES -- 1 A taste of likelihood -- 1.1 Introduction -- 1.2 Motivating example -- 1.2.1 ML estimation and inference for the binomial -- 1.2.2 Approximate normality versus likelihood ratio -- 1.3 Using SAS, R and ADMB -- 1.3.1 Software resources -- 1.4 Implementation of the motivating example -- 1.4.1 Binomial example in SAS -- 1.4.2 Binomial example in R -- 1.4.3 Binomial example in ADMB -- 1.5 Exercises -- 2 Essential concepts and iid examples -- 2.1 Introduction -- 2.2 Some necessary notation -- 2.2.1 MLEs of functions of the parameters -- 2.3 Interpretation of likelihood -- 2.4 IID examples -- 2.4.1 IID Bernoulli (i.e. binomial) -- 2.4.2 IID normal -- 2.4.3 IID uniform -- 2.4.4 IID Cauchy -- 2.4.5 IID binormal mixture model -- 2.5 Exercises -- Part II: PRAGMATICS -- 3 Hypothesis tests and confidence intervals or regions -- 3.1 Introduction -- 3.2 Approximate normality of MLEs -- 3.2.1 Estimating the variance of θ -- 3.3 Wald tests, confidence intervals and regions -- 3.3.1 Test for a single parameter -- 3.3.2 Test of a function of the parameters -- 3.3.3 Joint test of two or more parameters -- 3.3.4 In R and SAS: Old Faithful revisited -- 3.4 Likelihood ratio tests, confidence intervals and regions -- 3.4.1 Using R and SAS: Another visit to Old Faithful -- 3.5 Likelihood ratio examples -- 3.5.1 LR inference from a two-dimensional contour plot -- 3.5.2 The G-test for contingency tables -- 3.6 Profile likelihood -- 3.6.1 Profile likelihood for Old Faithful -- 3.7 Exercises -- 4 What you really need to know -- 4.1 Introduction -- 4.2 Inference about g(θ) -- 4.2.1 The delta method -- 4.2.2 The delta method applied to MLEs -- 4.2.3 The delta method using R, SAS and ADMB -- 4.2.4 Delta method examples. | |
| 880 | 8 | |6 505-00/(S |a 4.3 Wald statistics -- quick and dirty-- 4.3.1 Wald versus likelihood ratio revisited -- 4.3.2 Pragmatic considerations -- 4.4 Model selection -- 4.4.1 AIC -- 4.5 Bootstrapping -- 4.5.1 Bootstrap simulation -- 4.5.2 Bootstrap confidence intervals -- 4.5.3 Bootstrap estimate of variance -- 4.5.4 Bootstrapping test statistics -- 4.5.5 Bootstrap pragmatics -- 4.5.6 Bootstrapping Old Faithful -- 4.5.7 How many bootstrap simulations is enough-- 4.6 Prediction -- 4.6.1 The plug-in approach -- 4.6.2 Predictive likelihood -- 4.6.3 Bayesian prediction -- 4.6.4 Pseudo-Bayesian prediction -- 4.6.5 Bootstrap prediction -- 4.7 Things that can mess you up -- 4.7.1 Multiple maxima of the likelihood -- 4.7.2 Lack of convergence -- 4.7.3 Parameters on the boundary of the parameter space -- 4.7.4 Insufficient sample size -- 4.8 Exercises -- 5 Maximizing the likelihood -- 5.1 Introduction -- 5.2 The Newton-Raphson algorithm -- 5.3 The EM (Expectation-Maximization) algorithm -- 5.3.1 The simple form of the EM algorithm -- 5.3.2 Properties of the EM algorithm -- 5.3.3 Accelerating the EM algorithm -- 5.3.4 Inference -- 5.4 Multi-stage maximization -- 5.4.1 Efficient maximization via profile likelihood -- 5.4.2 Multi-stage optimization -- 5.5 Exercises -- 6 Some widely used applications of maximum likelihood -- 6.1 Introduction -- 6.2 Box-Cox transformations -- 6.2.1 Example: the Box and Cox poison data -- 6.3 Models for survival-time data -- 6.3.1 Notation -- 6.3.2 Accelerated failure-time model -- 6.3.3 Parametric proportional hazards model -- 6.3.4 Cox's proportional hazards model -- 6.3.5 Example in R and SAS: Leukaemia data -- 6.4 Mark-recapture models -- 6.4.1 Hypergeometric likelihood for integer valued N -- 6.4.2 Hypergeometric likelihood for N ε R+ -- 6.4.3 Multinomial likelihood -- 6.4.4 Closing remarks -- 6.5 Exercises. | |
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