Goodness-of-Fit Tests and Model Validity

This book thoroughly discusses statistical procedures to evaluate the assumptions of different distributions for the data observed, the validity of models such as linear models, generalized linear models, additive models, etc. and also to consider validity and justification of the use of robust statistical procedures. Professionals and researchers interested in reliability, applied statistics, statistical inference and statistical modeling will find this book an up-to-date reference and resource.

"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

Auteur
N. BALAKRISHNAN, PhD, is Professor of Mathematics and Statistics at McMaster University in Hamilton, Ontario, Canada.V. B. NEVZOROV, PhD, DS, is Professor of Probability and Statistics at St. Petersburg State University in St. Petersburg, Russia.

Contenu
I: History and Fundamentals.- 1 Karl Pearson and the Chi-Squared Test.- 2 Karl Pearson Chi-Square TestThe Dawn of Statistical Inference.- 3 Approximate Models.- II: Chi-Squared Test.- 4 Partitioning the Pearson-Fisher Chi-Squared Goodness-of-Fit Statistic.- 5 Statistical Tests for Normal Family in Presence of Outlying Observations.- 6 Chi-Squared Test for the Law of Annual Death Rates: Case with Censure for Life Insurance Files.- III: Goodness-of-Fit Tests for Parametric Distributions.- 7 Shapiro-Wilk Type Goodness-of-Fit Tests for Normality: Asymptotics Revisited.- 8 A Test for Exponentiality Based on Spacings for Progressively Type-II Censored Data.- 9 Goodness-of-Fit Statistics for the Exponential Distribution When the Data are Grouped.- 10 Characterization Theorems and Goodness-of-Fit Tests.- 11 Goodness-of-Fit Tests Based on Record Data and Generalized Ranked Set Data.- IV: Regression and Goodness-of-Fit Tests.- 12 Gibbs Regression and a Test of Goodness-of-Fit.- 13 A CLT for the L_2 Norm of the Regression Estimators Under ?-Mixing: Application to G-O-F Tests.- 14 Testing the Goodness-of-Fit of a Linear Model in Nonparametric Regression.- 15 A New Test of Linear Hypothesis in Regression.- V: Goodness-of-Fit Tests in Survival Analysis and Relability.- 16 Inference in Extensions of the Cox Model for Heterogeneous Populations.- 17 Assumptions of a Latent Survival Model.- 18 Goodness-of-Fit Testing for the Cox Proportional Hazards Model.- 19 A New Family of Multivariate Distributions for Survival Data.- 20 Discrimination Index, the Area Under the ROC Curve.- 21 Goodness-of-Fit Tests for Accelerated Life Models.- VI: Graphical Methods and General Goodness-of-Fit Tests.- 22 Two Nonstandard Examples of the Classical Stratification Approach to Graphically AssessingProportionality of Hazards.- 23 Association in Contingency Tables, Correspondence Analysis, and (Modified) Andrews Plot.- 24 Orthogonal Expansions and Distinction Between Logistic and Normal.- 25 Functional Tests of Fit.- 26 Quasi Most Powerful Invariant Tests of Goodness-of-Fit.- VII: Model Validity in Quality of Life.- 27 Test of Monotonicity for the Rasch Model.- 28 Validation of Model Assumptions in Quality of Life Measurements.- VIII: Tests of Hypotheses and Estimation with Applications.- 29 One-Sided Hypotheses in a Multinomial Model.- 30 A Depth Test for Symmetry Peter.- 31 Adaptive Combination of Tests.- 32 Partially Parametric Testing.- 33 Exact Nonparametric Two-Sample Homogeneity Tests.- 34 Power Comparisons of Some Nonparametric Tests for Lattice Ordered Alternatives in Two-Factor Experiments.- 35 Tests of Independence with Exponential Marginals.- 36 Testing Problem for Increasing Function in a Model with Infinite Dimensional Nuisance Parameter.- 37 The Concept of Generalized Asymptotic Deficiency and its Application to the Minimum Discrepancy Estimation.