Goodness-Of-Fit Tests and Model Validity

by Huber-Carol, C.; Balakrishnan, N.; Nikulin, M. S.; Mesbah, M.

• ISBN13: 9780817642099
• ISBN10: 0817642099
• Format: Hardcover
• Copyright: 2002-03-01
• Publisher: Birkhauser

Summary

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.

Table of Contents

Preface

Contributors

List of Tables

List of Figures

History and Fundamentals Karl Pearson and the Chi-Squared Test

The Dawn of Statistical Inference

Approximate Models

Chi-Squared Test Partitioning the Pearson-Fisher Chi-Squared Goodness-of-Fit Statistic

Statistical Tests for Normal Family in Presence of Outlying Observations

Chi-Squared Test for the Law of Annual Death Rates: Case with Censure for Life Insurance Files

Goodness-of-Fit Tests for Parametric Distributions Shapiro-Wilk Type Goodness-of-Fit Tests for Normality: Asymptotics Revisited

A Test for Exponentiality Based on Spacings for Progressively Type II Censored Data

Goodness-of- Fit Statistics for the Exponential Distribution When the Data are Grouped

Characterization Theorems and Goodness-of-Fit Tests

Goodness-of-Fit Tests Based on Record Data and Generalized Ranked Set Data

Regression and Goodness-of-Fit Tests

Gibbs Regression and a Test of Goodness-of-Fit

A CLT for the L_2 Norm of the Regression Estimators Under alpha-Mixing: Application to G-O-F Tests

Testing the Goodness-of-Fit of a Linear Model in Nonparametric Regression

A New Test of Linear Hypothesis in Regression

Goodness-of-Fit Tests in Survival Analysis and Reliability

Inference in Extensions of the Cox Model for Heterogeneous Populations

Assumptions of a Latent Survival Model

Goodness-of-Fit Testing of the Cox Proportional Hazards Model

A New Family of Multivariate Distributions for Survival Data

Discrimination Index, the Area Under to ROC Curve

Goodness-of-Fit Tests for Accelerated Life Models

Graphic Methods and General Goodness-of-Fit Tests

Two Nonstandard Examples of the Classical Stratification Approach to Graphically Assessing Proportionality of Hazards

Association in Contingency Tables, Correspondence Analysis, and (Modified) Andrews Plots

Orthogonal Expansions and Distinction Between Logistic and Normal

Functional Tests of Fit

Quasi Most Powerful Invariant Tests of Goodness-of-Fit

Model Validity in Quality of Life

Test of Monotonicity for the Rasch Model

Validation of Model Assumptions in Quality of Life Measurements

Tests of Hypotheses and Estimation with Applications

One-Sided Hypotheses in a Multinomial Model

A Depth Test for Symmetry

Adaptive Combination of Tests

Partially Parametric Testing

Exact Nonparametric Two-Sample Homogeneity Tests

Power Comparisons of Some Nonparametric Tests for Lattice Ordered Alternatives in Two-Factor Experiments

Tests of Independence with Exponential Marginals

Testing Problem for Increasing Function in a Model with Infinite Dimensional Nuisance Parameter

The Concept of Generalized Asymptotic Deficie

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