Goodness-Of-Fit Tests and Model Validity

ISBN-13: 9781461266136 / Angielski / Miękka / 2012 / 507 str.

C. Huber-Carol; N. Balakrishnan; M. Nikulin

Opis

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.

Recenzje

"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

Spis treści

Preface Contributors List of Tables List of Figures ---------------------- Part I. History and Fundamentals Karl Pearson and the Chi-Squared Test / D.R. Cox Karl Pearson Chi-Square Test—The Dawn of Statistical Inference / C.R. Rao Approximate Models / P.J. Huber -------------------- Part II. Chi-Squared Test Partitioning the Pearson-Fisher Chi-Squared Goodness-of-Fit Statistic / G.D. Rayner Statistical Tests for Normal Family in Presence of Outlying Observations / A. Zerbet Chi-Squared Test for the Law of Annual Death Rates: Case with Censure for Life Insurance Files / L. Gerville-Reache ------------------------ Part III. Goodness-of-Fit Tests for Parametric Distributions Shapiro-Wilk Type Goodness-of-Fit Tests for Normality: Asymptotics Revisited / P. Kumar A Test for Exponentiality Based on Spacings for Progressively Type II Censored Data / N. Balakrishnan, H.K.T. Ng, and N. Kannan Goodness-of- Fit Statistics for the Exponential Distribution When the Data are Grouped / S. Gulati and J. Neus Characterization Theorems and Goodness-of-Fit Tests / C.E. Marchetti and G.S. Mudholkar Goodness-of-Fit Tests Based on Record Data and Generalized Ranked Set Data / B.C. Arnold, R.J. Beaver, E. Castillo, and J.M. Sarabia ------------------------------- Part IV. Regression and Goodness-of-Fit Tests Gibbs Regression and a Test of Goodness-of-Fit / L. Seymour A CLT for the L_2 Norm of the Regression Estimators Under alpha-Mixing: Application to G-O-F Tests / C.A.T. Diack Testing theGoodness-of-Fit of a Linear Model in Nonparametric Regression / Z. Mohdeb and A. Mokkadem A New Test of Linear Hypothesis in Regression / Y. Baraud, S. Huet, and B. Laurent ------------------------------------- Part V. Goodness-of-Fit Tests in Survival Analysis and Reliability Inference in Extensions of the Cox Model for Heterogeneous Populations / O. Pons Assumptions of a Latent Survival Model / M.-L. Ting Lee and G.A. Whitmore Goodness-of-Fit Testing of the Cox Proportional Hazards Model / K. Devarajan and N. Ebrahimi A New Family of Multivariate Distributions for Survival Data / S.T. Gross and C. Huber-Carol Discrimination Index, the Area Under to ROC Curve / B.-H. Nam and R. B. D'Agostino Goodness-of-Fit Tests for Accelerated Life Models / V. Bagdonavicius and M.S. Nikulin ------------------------------ Part VI. Graphic Methods and General Goodness-of-Fit Tests Two Nonstandard Examples of the Classical Stratification Approach to Graphically Assessing Proportionality of Hazards / N. Keiding Association in Contingency Tables, Correspondence Analysis, and (Modified) Andrews Plots / R. Khattree and D.N. Naik Orthogonal Expansions and Distinction Between Logistic and Normal / C.M. Cuadras and D. Cuadras Functional Tests of Fit / D. Bosq Quasi Most Powerful Invariant Tests of Goodness-of-Fit --------------------------------- Part VII. Model Validity in Quality of Life Test of Monotonicity for the Rasch Model J. Bretagnolle Validation of Model Assumptions in Quality of Life Measurements / A. Hamon, J.F. Dupuy, and M. Mesbah