Goodness-of-Fit Tests and Model Validity

Front Matter....Pages i-xxxv
Front Matter....Pages 1-1
Karl Pearson and the Chi-Squared Test....Pages 3-8
Karl Pearson Chi-Square Test The Dawn of Statistical Inference....Pages 9-24
Approximate Models....Pages 25-41
Front Matter....Pages 43-43
Partitioning the Pearson-Fisher Chi-Squared Goodness-of-Fit Statistic....Pages 45-55
Statistical Tests for Normal Family in Presence of Outlying Observations....Pages 57-64
Chi-Squared Test for the Law of Annual Death Rates: Case with Censure for Life Insurance Files....Pages 65-70
Front Matter....Pages 71-71
Shapiro-Wilk Type Goodness-of-Fit Tests for Normality: Asymptotics Revisited....Pages 73-88
A Test of Exponentiality Based on Spacings for Progressively Type-II Censored Data....Pages 89-111
Goodness-of-Fit Statistics for the Exponential Distribution When the Data are Grouped....Pages 113-123
Characterization Theorems and Goodness-of-Fit Tests....Pages 125-142
Goodness-of-Fit Tests Based on Record Data and Generalized Ranked Set Data....Pages 143-157
Front Matter....Pages 159-159
Gibbs Regression and a Test for Goodness-of-Fit....Pages 161-172
A CLT for the L_2 Norm of the Regression Estimators Under α-Mixing: Application to G-O-F Tests....Pages 173-184
Testing the Goodness-of-Fit of a Linear Model in Nonparametric Regression....Pages 185-193
A New Test of Linear Hypothesis in Regression....Pages 195-207
Front Matter....Pages 209-209
Inference in Extensions of the Cox Model for Heterogeneous Populations....Pages 211-225
Assumptions of a Latent Survival Model....Pages 227-235
Goodness-of-Fit Testing for the Cox Proportional Hazards Model....Pages 237-254
A New Family of Multivariate Distributions for Survival Data....Pages 255-265
Discrimination Index, the Area Under the ROC Curve....Pages 267-279
Front Matter....Pages 209-209
Goodness-of-Fit Tests for Accelerated Life Models....Pages 281-297
Front Matter....Pages 299-299
Two Nonstandard Examples of the Classical Stratification Approach to Graphically Assessing Proportionality of Hazards....Pages 301-309
Association in Contingency Tables, Correspondence Analysis, and (Modified) Andrews Plots....Pages 311-326
Orthogonal Expansions and Distinction Between Logistic and Normal....Pages 327-339
Functional Tests of Fit....Pages 341-356
Quasi Most Powerful Invariant Tests of Goodness-of-Fit....Pages 357-361
Front Matter....Pages 363-363
Test of Monotonicity for the Rasch Model....Pages 365-370
Validation of Model Assumptions in Quality of Life Measurements....Pages 371-383
Front Matter....Pages 385-385
One-Sided Hypotheses in a Multinomial Model....Pages 387-399
A Depth Test for Symmetry....Pages 401-412
Adaptive Combination of Tests....Pages 413-424
Partially Parametric Testing....Pages 425-433
Exact Nonparametric Two-Sample Homogeneity Tests....Pages 435-448
Power Comparisons of Some Nonparametric Tests for Lattice Ordered Alternatives in Two-Factor Experiments....Pages 449-462
Tests of Independence with Exponential Marginals....Pages 463-476
Testing Problem for Increasing Function in a Model with Infinite Dimensional Nuisance Parameter....Pages 477-493
The Concept of Generalized Asymptotic Deficiency and its Application to the Minimum Discrepancy Estimation....Pages 495-503
Back Matter....Pages 505-507