PRINCIPLES OF STATISTICAL INFERENCE - GBV

1 Advanced Series onStatistical Science &Applied ProbabilityPRINCIPLES OFSTATISTICALINFERENCE from a Neo-Fisherian PerspectiveLuigi PaceDepartment of StatisticsUniversity ofUdine, ItalyAlessandra SalvanDepartment of StatisticsUniversity of Padua, ItalyWorld ScientificSingapore'New Jersey London'Hong KongCONTENTSPREFACE xvLIST OF SYMBOLS xvii1 STATISTICAL MODELS The Theory of STATISTICAL INFERENCE Four Paradigms of INFERENCE Model Specification Levels of Specification

2 Notes on the Specification of a Parametric Model .. Parametric STATISTICAL Models and Likelihood General Formulation of a STATISTICAL Model Likelihood and Related Quantities Reparameterizations Examples of Likelihood Functions Bibliographic Note Problems 292 DATA AND MODEL REDUCTION

3 Introduction Statistics Distribution Constant Statistics Sufficient Statistics > Completeness Conditioning on Distribution Constant Statistics Discussion and Examples Ancillary Statistics Relevant Subsets Combinants and Pivotal Quantities 58viiviii The Principle of Parameterization In variance Consequences for Parameter Estimation Consequences for Hypothesis Testing Uninformative Prior Distributions and Invariance.

4 Bibliographic Note Problems 673 SURVEY OF SOME BASIC CONCEPTSAND TECHNIQUES Introduction Moments, Cumulants and their Generating Functions The Moment Generating Function The Characteristic Function Convergence Results Generating Functions for Sums The Cumulant Generating Function Infinitely Divisible, Stable, Selfdecomposable Laws.

5 Multivariate Extensions Basic Notions of Asymptotic Methods Orders of Magnitude of Sequences Convergence of Sums and Extremes Orders in Probability: Examples Likelihood and First-Order Asymptotic Theory Null Asymptotic Distributions Non-null Asymptotic Distributions Robustness of Likelihood Methods 94- - INFERENCE in the Frequency-Decision Paradigm General Framework Point Estimation Testing Hypotheses

6 Confidence Regions": Comments on the Relations with Likelihood INFERENCE . The Empirical Distribution Function Basic Properties Nonparametric Maximum Likelihood Estimate STATISTICAL Functional Bibliographic Note Problems 118 CONTENTS ix4 NUISANCE PARAMETERS ANDPSEUDO-LIKELIHOODS

7 Nuisance Parameters Data and Model Reduction with Nuisance Parameters Lack of Information: No Nuisance Parameters Lack of Information in the Presence of Nuisance Param-eters Weaker Concepts of Lack of Information with NuisanceParameters Nuisance Parameters and Reparameterizations The Notion of a Pseudo-Likelihood Marginal Likelihood: Examples Conditional Likelihood.

8 Examples Profile Likelihood Orthogonal Parameterization and Approximate Conditional Like-lihood Partial Likelihood Quasi-Likelihood Empirical Likelihood Bibliographic Note Problems 1665 EXPONENTIAL FAMILIES Introduction Exponential Families of Order 1 Mean Value Mapping and Variance Function Multiparameter Exponential Families Definitions and Basic Results Independence, Marginal and Conditional Distributions.

9 Sufficiency and Completeness Likelihood and Exponential Families Profile Likelihood and Mixed Parameterization Procedures with Finite-Sample Optimality Properties Testing Hypotheses: One-Parameter Case Testing Hypotheses: Multiparameter Case First-Order Asymptotic Theory Curved Exponential Families Bibliographic Note . 217x Problems 2186 EXPONENTIAL DISPERSION FAMILIESAND GENERALIZED LINEAR MODELS Introduction Exponential Dispersion Families Parameterization (/z, a2)

10 And Convolution Properties Generalized Linear Models Likelihood and Sufficiency Quasi-Likelihood Deviance Tests Generalized Linear Models for Binary Data Bibliographic Note Problems 2537 GROUP FAMILIES Introduction Groups of Transformations Orbits and Maximal Invariants Simple Group Families Composite Group Families