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.