Goodness-of-Fit Tests and Model Validity

1. Front Matter

   Pages i-xxxv

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2. History and Fundamentals

   1. Front Matter

      Pages 1-1

      PDF

   2. Karl Pearson and the Chi-Squared Test

      • D. R. Cox

      Pages 3-8

   3. Karl Pearson Chi-Square Test The Dawn of Statistical Inference

      • C. R. Rao

      Pages 9-24

   4. Approximate Models

      • Peter J. Huber

      Pages 25-41

3. Chi-Squared Test

   1. Front Matter

      Pages 43-43

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   2. Partitioning the Pearson-Fisher Chi-Squared Goodness-of-Fit Statistic

      • G. D. Rayner

      Pages 45-55

   3. Statistical Tests for Normal Family in Presence of Outlying Observations

      • Aïcha Zerbet

      Pages 57-64

   4. Chi-Squared Test for the Law of Annual Death Rates: Case with Censure for Life Insurance Files

      • Léo Gerville-Reache

      Pages 65-70

4. Goodness-of-Fit Tests for Parametric Distributions

   1. Front Matter

      Pages 71-71

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   2. Shapiro-Wilk Type Goodness-of-Fit Tests for Normality: Asymptotics Revisited

      • Pranab Kumar Sen

      Pages 73-88

   3. A Test of Exponentiality Based on Spacings for Progressively Type-II Censored Data

      • N. Balakrishnan, H. K. T. Ng, N. Kannan

      Pages 89-111

   4. Goodness-of-Fit Statistics for the Exponential Distribution When the Data are Grouped

      • Sneh Gulati, Jordan Neus

      Pages 113-123

   5. Characterization Theorems and Goodness-of-Fit Tests

      • Carol E. Marchetti, Govind S. Mudholkar

      Pages 125-142

   6. Goodness-of-Fit Tests Based on Record Data and Generalized Ranked Set Data

      • Barry C. Arnold, Robert J. Beaver, Enrique Castillo, Jose Maria Sarabia

      Pages 143-157

5. Regression and Goodness-of-Fit Tests

   1. Front Matter

      Pages 159-159

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   2. Gibbs Regression and a Test for Goodness-of-Fit

      • Lynne Seymour

      Pages 161-172

   3. A CLT for the L_2 Norm of the Regression Estimators Under α-Mixing: Application to G-O-F Tests

      • Cheikh A. T. Diack

      Pages 173-184

   4. Testing the Goodness-of-Fit of a Linear Model in Nonparametric Regression

      • Zaher Mohdeb, Abdelkader Mokkadem

      Pages 185-193

   5. A New Test of Linear Hypothesis in Regression

      • Y. Baraud, S. Huet, B. Laurent

      Pages 195-207

The 37 expository articles in this volume provide broad coverage of important topics relating to the theory, methods, and applications of goodness-of-fit tests and model validity. The book is divided into eight parts, each of which presents topics written by expert researchers in their areas. Key features include: * state-of-the-art exposition of modern model validity methods, graphical techniques, and computer-intensive methods * systematic presentation with sufficient history and coverage of the fundamentals of the subject * exposure to recent research and a variety of open problems * many interesting real life examples for practitioners * extensive bibliography, with special emphasis on recent literature * subject index This comprehensive reference work will serve the statistical and applied mathematics communities as well as practitioners in the field.

• Estimator
• Extension
• Plot
• Regression
• Survival analysis
• best fit
• calculus
• linear modeling
• linear optimization
• mathematics
• mixing
• model
• statistical inference
• statistical modeling
• statistics

"The book contains a great number of the most recent references, is full of new ideas and approaches, original test proposals, graphical representations, examples of real data (mainly from medical science) and useful tables, and it demonstrates clearly how inspiring can the celebrated KP's paper be even after 100 years."   —Applications of Mathematics

"This unique and interesting volume of 37 articles, commemorating the centennial anniversary of the landmark paper by Karl Pearson (1900) on chi-square goodness-of-fit tests, presents a broad spectrum of papers.... The background history of Pearson's paper is thoroughly covered as well as the fundamentals of this very important topic. These articles, many of them written by renowned experts in this area, discuss modern model validity methods, graphical techniques, recent research in the area of goodness-of-fit tests, and numerous real-life examples. The volume is divided into eight major areas: history and fundamentals, chi-squared tests, goodness-of-fit for parametric distributions, regression and goodness-of-fit tests, goodness-of-fit tests in survival analysis and reliability, graphical methods and general goodness-of-fit tests, model validity in quality of life, and tests of hypothesis and estimation with applications. Highly recommended for upper-division undergraduates through practitioners."   —Choice

• Laboratoire de Statistique Médicale, Université Rene Descartes-Paris 5, Paris, France

  C. Huber-Carol

• Department of Mathematics and Statistics, McMaster University, Hamilton, Canada

  N. Balakrishnan

• Laboratoire Statistique Mathématique, Université Bordeaux 2, Bordeaux Cedex, France

  M. S. Nikulin

• Laboratory of Statistical Methods, V. Steklov Mathematical Institute, St. Petersburg, Russia

  M. S. Nikulin

• Laboratoire de Statistique Appliquée, Université de Bretagne Sud, Vannes, France

  M. Mesbah

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