Goodness-of-Fit Tests and Model Validity

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.

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.

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.

I: History and Fundamentals.- 1 Karl Pearson and the Chi-Squared Test.- 2 Karl Pearson Chi-Square Test-The 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.