Goodness-of-Fit Tests and Model Validity

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.

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.